It is not about whether or not you are competing or whether you have a competitive nature. A pickup basketball game is not the NBA finals and people who treat it like that are douchebags.
This is how I feel. You aren't competing for anything, and there is a 99.9 percent chance that nobody in your game is even good enough to play at a competitive level. But they get mad like they would have totally won every game ever but they have a bad teammate...
And it is a video game. If you aren't having fun, it is probably time to put it down.