Can't comment on 'Nazi Zombies' - I believe it's a user made modification and not an official release. But...
My family are all gamers. My children are a little younger and still at the Little Big Planet/Animal Crossing age.
But I think MrsFlux raises a pertinent question.
I don't give my children Modern Warfare to play, but they have occasionally seen me or DH playing that, or Grand Theft Auto.
The main issues for me are fear and nightmares and imitable behaviour.
Re: Fear... I've actually found they self-censor what they watch. If something is too scary, they make a decision to walk away. I can imagine with a group of boys though, there is peer pressure to play. That said, Dr Who scares me (and them) more than any game has.
As far as imitable behaviour goes... I think this is VERY complex and most research is far too simplistic. Some children will imitate behaviour from video games and tv shows. Some won't. It also depends how the behaviour is framed the game, how repetitive it is, how much the children identify with it...
Personally, I think with guidance from parents, they will have more of an idea what is allowable in the real world and what is only allowed in fantasy play or not allowable at all.
In fact, I see Modern Warfare as quite a good opportunity to talk to them about war and terrorism (and probably with a bias towards my own bleeding heart liberal values).
To be honest, my stepfather watched high bodycount Schwarzenegger and Stallone movies all day long when I was a child. I just found them boring.