How do your characters game? And when they fail, how do they react? Maybe their rage is the silent, cool anger, or just furious screeching paired with enemy trashing. It could also be a process that goes from the former to the latter. How long do they last anyway before rage quitting?
If you want to make their reaction specific to a game, then it can be any kind of game, whether it be board game monopoly or even Battle Royale. You can even pull in Flappy Bird.
My protagonist, Kaede, plays mostly video games. With/against strangers, he doesn't really care. But against friends, he's easily a tryhard. Poor guy lets his sanity deteriorate until he gets at least one win/ kill of whoever keeps destroying him. Starts out with heavy sighs, then raising his brows real high. It goes on to music to either pump him up or calm him down (if his browser isn't slow). It doesn't take him long before he's reached madness with cursing inanimate objects, enemy trashing and furious mouse-slamming.
He lasts long playing, but his sanity doesn't.
he's in here ^