Would non-violent/competitive games also attract users more passionate for their games too? In that case competitive becomes synonymous with "games that attract passionate users", and the violent vs non-violent distinction is moot.

Else, "competitive" is irrelevant, and it's the "violent" part that matters. In which case, my argument holds: I don't see any reason to believe users of non-violent games are less passionate about their games.

And why would violent games be any more competitive than e.g. Chess, or Poker games, or some multiuser strategy game?