Look, bottom line, "kids today" shouldn't be playing GTA, since it's just not appropriate. That's a parent's responsibility. But if the kids sneaks in a few rounds at a friend's house, it's still not going to turn them into murderers. They may act out in imitation. I have no doubt about that. But it's a big leap between imitating (just as I too played "cops n robbers" as a kid, complete with toy cap-guns), and inflicting pain on another.
What DOES promote and cause child violence is anger, hatred and ignorance. A child who is angry will lash out. A child who hates, will lash out. And without proper guidance from adults, the boundaries of right and wrong aren't so clear. Empathy of another is taught. You teach a kid to not squeeze the kitty like that, and you teach them why. You teach kids to "imagine themselves in other's shoes". Without that teaching, they just won't care. Where things break down and cross the line is when kids are so angry and/or brought up to just not care about another's pain and suffering. They may cross the line. They may even do so while imitating something they saw, but the movie, or game is not the CAUSE. Talk about "desensitizing to violence" all you want, it's not the motive for inflicting pain on another.
Raise a kid in an environment where he feels worthless, like he has nothing to lose, and a lot of bad things can happen.