If you look at the hours played per user grand strategy games and simulations seem to be on the front row. And grand strategy gamers are probably one of the most balanced individuals I've met.
The only definition that I could come up for in the few minutes I spent thinking about it is that the "usual" flaming, hating and insulting gamers just seem to have an unhealthy emotional balance. Some of these I know in "real life" seem to be very disconnected from emotions "offline". But as soon as they turn on the computer, they release all of these stored emotions.
But why, as you imply, more violent games would attract people "who care more about the games they play" (over other types of games)?
Don't e.g. chess players care as much "about the games the play", perhaps more so than some violent FPS player in times spent? Or RPG players?
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?
For example they play a battle royale genre game and 20-30 minutes into a match they are one of two teams left and then die blaming some perceived thing that happened like game physics getting in the way, it appears they were shot through a wall, etc. The immature gamer (aka 10-20 years old and maybe beyond) may believe their talents are greater than reality.
This goes beyond age and is common outside of just competitive gaming. In the work place you see plenty of people who think e.g. manager's or other departments don't do anything, that they could run the company better, etc etc. On the flipside, I love hearing about people (in e.g. Overwatch) who get stuck at some ranking, hit a breaking point where they stop blaming others and focus on themselves, then slowly start to ascend.