There are three reasons:

1. Games themselves are competitive area. Especially with the rise of internet, you can notice biggest communities are gathereing around inherently competitive games, in which players are pit one against eachother, either solo, in teams or in broader factions. This turn their brain into tribal mush pudding, very much like the football or other team sports, which as you surely know have their share of very loud and/or violent fans.
2. People immersed so much that they indentify themselves as "gamers", often have social problems etc. etc. this is talked ad nauseam everywhere. Which in turn makes them vulnerable to point 1.
3. Deciding factor - fash propaganda noticed that first, and did what the fash specialised themselves since 100 years already - made massive propaganda attack on those vulnerable people.

Medium itself is not to blame here (though we surely do need so communist games or games where communism isn't shown as evil, but that's more of a capitalism problem). They were just ideologically much of tabula rasa, which got a fucking big swastika drawn on before anyone else noticed.