It depends. By the time the child is, say, ten years old, it should realize that hurting people is always a bad, destructive thing. That understanding should prevent it from becoming violent.
I often don't agree with the age restrictions on games. Usually, whenever bloodshed is shown, the game is considered too violent for teenagers, and gets an 18+ rating.
I saw Mortal Kombat being played when I was eight or nine, and I knew that what the characters were doing was a bad, disgusting thing. If anything, it's made me less squeamish about blood, and less easily shocked by violence in games.
Blaming violent behavior on video games is often a convenient way to shift the blame from the parents' inadequate parenting and the environment.