But I probably would not let my hypothetical kids play with violent video games, even if I had no guns.

Nor would I.

Though, there's another way to go about that:

"For every person you shoot in that game, you have to look at a picture of a real shooting victim and watch to a real video of the victim's family, immediately before going to bed.” (This will predictably cause nightmares where the kid is the victim of violence. Good. Dreams aren’t “real” either, but they do have teaching-value.)