I think it depends on the child and the situation. I also played a lot on the computer as a child (Warcraft I + II, Baldurs Gate, Doom ^^) but my mother told me, that she was not really worrying about me, because when she came in and started to talk about me about the game I seemed to be very happy and the games seemed to relax me.
If you start to ask your child about, what he/she is playing, and what it feels because of it and its telling you frustrated about that "damned noob lamer" that ruins everything and so on, and so on... and everyone sucks..... in a way that you can feel frustration, anger and so on behind the words, i would worry.
So a game should be for fun and playing it should bring fun. But if its played to wioe out anger and frustration it would worry me. Because if someone plays to lower his anger and frustration, then it means that something is worrying him. And if something is deeply worrying you, gaming wont help you to solve your problem. So gaming should be for fun, not for hiding before problems.
If a 12 year old is able to recognize, that Shooters is nothing else then playing a ball game, where the player who gets hit has to leave the playfield for some minutes or so, I see no problem. If not, he should not play it.
Anyway, i think 12 year old should not play alone around 2:00 in the morning, what happened to me more than once. Today many games are also with a voice chat, and I dont think i wanted my 12 year child to be in a random voice chat. Not because of pedophiles, you are normally in bigger teams with at least 4 persons, i would be more afraid of the typical "He, i just got my first hair in my balls, so I have to proof that I am a man now, and as a man I have to use as many rude words as possible." teenager.
But from my Opinion you cannot say "Game xyz makes you violent" and "Game bnj not." The boy of the neighbors and I were lying on the floor laughing when we found out the cheats for the "Fatality" Kills for Mortal Combat. Some were really ridiculous. ^^ But we just laughed over it, as if it was Tom and Jerry. It would be something else for me, if someone would do this to a playpartner and then would be cheering, "...that this Lamer now got what he deserved" or so...
So shortly. I think the emotions someone has when playing are the most important part to decide if a game fits for your child or not. Sadly many parents do not care for the games their children plays. At christmas, when I was searching for a present for my partner in the videogame department of our electronic shop, there was a grandfather who simply asked other people that was interested in the same game he wanted to buy for his grandchild, if they could explain the game for him, so what you do in the game, and so on. I found that really responsible.