Some examples of the games we play but are not limited to are...
League of Legends
League of Legends is a MOBA (Multiplayer Online Battle Arena) in which two teams of five try to destroy the enemy base by progressing through three guarded lanes. Players control champions who have various advantages and disadvantages that force players to work together and communicate in order to win.
Overwatch is a team-oriented FPS (First Person Shooter) in which players control a "Hero" that has their own advantages, disadvantages, and role in a team to help win a match. The keyword here is team, as players can't win matches by themselves. Players can swap heroes in the middle of a match in order to counter the opponent and play a game of advanced rock paper scissors.
Super Smash Bros
Super Smash Bros. is a fighting game that's easy to get into, but hard to master. It contains video game characters from different franchises who all have their own special abilities based off the origin of the game they come from, with the simple goal of trying to knock other players off the screen. That being easier said than done, because this game requires skills in prediction as well as precise movement and timing in order to make sure your opponent doesn't do the same to you.
Hearthstone is an online CCG (Collectible Card Game) in which players control classes who all have access to their card pool, as well as a neutral set in which every class has access to, in order to build a deck of thirty cards and challenge other players with their own decks. This game challenges quick and critical thinking to outsmart your opponent and know your chances of winning.
Rainbow Six: Siege
Tom Clancy's Rainbow Six: Siege is a tactical FPS in which players rely on quick reactions, precise aim, smart positioning, and effective communications with teammates in order to either eliminate the enemy team, or play the objective, in order to win consecutive rounds in both defensive and offensive game modes. Players are limited to characters known as "Operators" who can only be played on either offense or defense in order to supply utility to their team.
Counter-Strike: Global Offensive is a tactical FPS who's popularity inspired games such as the one above that relies quick reactions, precise aim, smart positioning, effective communication, as well as some management due to the in-game money system that the game uses to award players based off of how well they're doing in order to prepare between rounds. There are no special characters in this game, it gives everyone an even playing field.