Parents are children's mirrors. Why do you think this idiom was created? Kids tend to follow everything that their parents do. Even if it's not a parent, they tend to follow whatever others are doing, that's their age group of life that does those.
If they see someone killing someone, they'd follow the same way as they might think that's alright to do so. They may follow them inside the game world, but what if they do that in the real world? Children might lose their sense of fake and real world. And the crime comes from those circumstances. To talk further, this could call up a victim of teenager protection policy.
What I think is that parents should be taking care of their children on playing violent games, kids should be left as a kid, not something that loosely follows adults and act like an adult.
There is no real proof that i could find (that hasn't been debunked) that shows that violent video games have any real correlation with real violent behaviors. Also many people including children know whats right from wrong, So unless the parents completely fail at telling the child that killing/hurting people is wrong. Which is honestly hard to do as its part of our culture and many more forms of media do not encourage this and say why its wrong to the point where its almost impossible to avoid. Also most people ( unless they have a mental illness) understand empathy and know why its impotent not to badly harm others.