Introduction
Video games have been a part of since it began. In my 14 years of experience I've learned a lot about them. One thing I know is that there is a game genre for every person. There are too many genres to list, so I picked notable ones, and avoided genres that are platform specific. My goal here is to help identify which genres are for which people.
MOBA
MOBA's or Multiplayer Online Battle Arena games are traditionally 5v5 on a square map. It is divided into 2 areas(one for each team) with a diagonal line. There are 3(Top, Mid, Bot) lanes with towers for each team in the lanes. There is also a jungle where monsters spawn. By killing anything you receive gold. Gold is used to buy items at the spawn. The goal is to make it to the the other team's base and destroy their core. You get to the base by traveling through any lane and destroying the towers in said lane, and that unlocks the ability to destroy the core. The game punishes dying harshly with long respawns. Every champion has special abilities and an ultimate that are on timers which get unlocked/upgraded after leveling up in a game by earning XP by doing something to contribute to your team in any way.
MOBA matches are normally long and require long term strategies to win. If you enjoy long-term planning then MOBA's would be fun for you. These games are all strategy by you being forced to manage your items, your life, your gold, your abilities, and your objective. In the early game there is a lot of stalemating with there being 1v1 fights in the lanes with the other 2 players playing support or running around the jungle to get gold. Eventually one team in one lane can make it to the other team's base which then leads to both teams hiding under towers until they are ready for big 5v5 fights until one team wins. These games involve a lot of team coordination, and planning. If you enjoy long-term strategies, and teamwork then MOBAs should be very fun.
RPG
RPG games are very unique because there are different versions of RPGs. There are Action RPGs(ARPG) that use real time combat, turn based RPGs like Pokemon, and too many more to name. The one element unifying them all is the Role-Playing element. In an RPG you take control of a character in some fictional universe. The story becomes yours because you become the character in a different way then an Adventure game. RPGs want you to feel like the character, while Adventure games want you to engage in its story.
I would recommend RPGs for people that enjoy characters and strategy. RPGs have always had strategy be a part of the formula because most RPGs let you customize your character, and that leads to a lot of strategy. Some RPGs have a skill tree, and games like Pokemon let you choose which pokemon you fight with. You can also enjoy RPGs if you enjoy the characters. If you enjoy the idea of being a 11-year old getting to start on your Pokemon adventure, then you would enjoy Pokemon. RPGs are meant for players that want to role play.
Shooters
The shooter genre is my favorite genre of video game, so this is going to be the most biased review/recommendation of them all. Shooter games have existed for a while, with most being multiplayer. The difference between a mulriplayer game and a singleplayer game is small because a shooter game is defined in its balance between gunplay and movement. My favorite game ever is TF2 and it is a First Person Shooter. I would describe it as a 50/50 split between gunplay and movement because every fight revolves around your ability to move and shoot equally. This isn't true in the other shooter game I play a lot, Rainbow Six Siege. The game heavily focuses on gunplay because of its one-shot headshot mechanic, and lack of dodging.
For a general overview of the genre, then you have to enjoy shooting in video games to enjoy shooter games. I know that sounds stupid and unhelpful, but there is a very big difference between shooting a gun in a game vs. punching. It relies heavily on the mouse(or aim assist that the game gives you on console), because everything revolves around it. If you don't like using your mouse a lot, then you probably wouldn't enjoy the shooting part of shooter games. If you want to get really specific about what kind of shooter you want to play, then you need to identify if you want to use mobility or gunplay more. If you like a tactical shooter with minimal movement, then R6 Siege is the game for you. Quake is a shooter designed to focus heavily on movement with the hole game revolving around it. Games like TF2(or Overwatch if you don't want to learn TF2's complex movement mechanics) is for players that enjoy a balance between shooting and movement.
Indie/Adventure
The Indie genre is an actual game genre, but it doesn't categorize games the same way saying a game is a PFS does. Indie games are games that are made by one person or a small group of people. FNAF was made by Scott Cawthon, and Undertale was made by Toby Fox. Adventure games are easy to define if you rename the genre. Adventure games follow a story that the developer made up, with one exception. Adventure games are designed for you to follow and get engaged in its story. The Indie game Undertale did a great job of this. The exception I mentioned earlier is when the developer has the player make the story. This is used in Minecraft by letting you go on whatever adventure you want to go on. The game does have an ending, but it was designed to be vague and apply to any story you made.
Indie games are for people that enjoy games with the touch that only an Indie developer can give. With the right developer, then these games can just ooze charm. If you like enjoying people's passion projects then you would love the work that is spent on these games. Adventure games are for players who enjoy stories. Adventure games are meant to engage you in the story it tells you. It wants you to feel like you are a part of its world. It wants you to get attached to its world. If you want to be the protagonist of a story, then these games are for you.
Sports
Sports game traditionally fall into 2 categories. They are either sports simulators like FIFA, or games that take a fun spin on sports/use the sport as a base for their game. The simulator games have been around since the Atari 2600. Games like Mario Kart, which got released on the SNES first, takes traditional racing games and tries to introduce new mechanics to make their game more fun. Rocket League is a unique sports game because it takes the sport soccer and recreates it in a fun and unique way. It is 3v3 soccer, but you are playing in cars with a boost mechanic.
Simulator sports games try to recreate how the sport works in real life. I would recommend simulator sports games for people that enjoy the mechanics of a sport while enjoying playing on a controller. Games like Mario Kart are designed to be fun for multiple people, so I would suggest only using it for when you have friends over. It does have skill mechanics in it, but these games are designed to be multiplayer games, and not an individual one. Sports games similar to Rocket League are fun for players that enjoy sports or players that like technical skill. These games have to make their movement from scratch while having a similar skill ceiling to normal sports. It feels like playing a brand new sport, but with a controller/keyboard and mouse.
Horror
Horror games start off by teaching you how to play their game, then you have to survive from whatever the scary thing is in the game. The game does get more difficult, and forces you to get better at whatever you were doing in the beginning. This is different from a new technique being created out of old ones, this is getting better at closing doors(one mechanic in Five Nights at Freddy's). These games are normally famous for their stories and its scary feature. FNAF did this by causing the gaming community to theorize about its story while people loving the animatronics and their jumpscares(in the early days of FNAF).
Horror games are for people who enjoy stories, and people who want to get scared. You would play these games for the same reasons you would watch a horror movie. These games also attract people who enjoy stories, by having their scary thing be related to it. This leads to some players wanting to learn more about the world and knowing why there are 5 killer animatronics in FNAF. I would recommend Horror games for people who enjoy scary, and for people who enjoy solving mysteries without being terrified of the game.
Platformer
Most platformers are getting from point A to point B, but with gimmicks. In Mario games there are power-ups which give the player a boost in some way. My current favorite platformer is Celeste because it has a dash mechanic which allows for some insane movement. This is one of the game genres that does involve stages as a progression system. Some platformers do involve combat, but it isn't a requirement. Celeste has a small amount of enemies, but the solution to defeating them is always dodging them until you beat the level.
It is hard to recommend this genre, at least for me, because games like Mario and Celeste play very differently. For me it is about finding which game mechanic interests you. If you like the idea of power ups, and jumping on enemies to defeat them, then you would love the Mario series. If you want to know if any platformer is a good fit for you, then you need to ask yourself if you enjoy progressing in a game by moving to a certain point on the stage, enjoy using whatever tools the game gives you to get the end of the level, and thinking on the spot to problems that occur.
Battle Royale
The Battle Royale genre has become the current popular game genre. Many agree that it originated from Minecraft after someone made a game in Minecraft based off The Hunger Games. In this game players are spawned at the cornucopia, and then have to find resources and try to be the last man standing. In 2017, Bluehole made Player's Unknown Battle Grounds or PUBG for short. This was the first game in the Battle Royale craze. It got followed by Fortnite, then CS:GO and CoD both released Battle Royale versions of their games. The latest game in this craze is Apex Legends.

In Battle Royale games, you get the power to choose your spawn location on a big map, work in a small squad or solo, and be forced to find weapons and ammo. Mobility in Battle Royales are normally used to get from point A to point B, with the ability to be used in combat less effectively. Battle Royales favor a passive playstyle, but it gets really boring and repetitive. As a result, players prefer agressive playstyles to shorten the time of matches, and have more unique matches. I would recommend Battle Royales for players that enjoy agressive playstyles, but without having any goal or objective other than surviving.
Fighting
Most fighting games are 2d with their fighters being existing characters. The Super Smash Bros. and Injustice series are a good example of this. The background barely moves, and is just some platforms on a screen. 3d fighting games normally play on a flat circular stage, which makes them play differently compared to their 2d counterparts. There is also a bigger focus on aiming because there is a 3rd direction to move in. Fighting games also consist of a core set of move types that every fighter has a different version of. One example is the special attacks in Super Smash Bros. Mario's neutral special is a fireball, and Pikachu's is thunderjolt. It's the same input on a controller, but it does different things on different characters.
Fighting games traditionally are 2d, with some examples trying a 3d world. Mobility is normally a big factor in matches, but unlike most games its mobility only occurs in fights. However fighting games force players to always fight with a small screen. Fighting games are also very technical with combos, grabs, and frame perfect attacks. Watching any pro match, shows how much control the pros have over their characters to allow for fast mobility and combos that are impossible to escape from. I would recommended fighting games for people that enjoy either casual fun or highly technical gameplay.