@JAF: Or Killing Floor. Or Left 4 Dead. Or Zombie Panic! Source.
Then again, he/she is too young for these.
@Nyarly: Stubbs was never submitted to the USK as far as I know. It's a bit of a gamble; if a game is submitted and denied classification, it is usually banned shortly after and can only be sold on request while non-classified games fall under the default 18+ classification. It could still be banned but that is less likely as it would be through the classification process.
How good is his computer?
Dead Frontier is a decent browser shooter/MMO, and if his computer has Half Life 1, try getting They Hunger.
Half-Life: Dual Nature, a crossover story of reasonably sized proportions.Ocarina Of Time. It's done without making them ridiculously scary, yet still fairly creepy.
Sure it's not a pure zombie game, but... Also, it's a lot of fun and right around his age anyway.
Quest 64 thread

I think we should propose to Pop Cap a zombie version of Peggle.