In relation to the recent release of the Charlie Kaufman film Anomalisa, and the review above, I started thinking about this. In the review Kermode says that "it's not a family film, it's not for children". I haven't seen the film, but I've seen reviews of it, and I understand what he means. I remember when that phrase was said to me as a kid, and back then it basically meant "it's got lots of violence or it's really scary" to me. But growing up I actually started to understand what it really means: it's not meant for children necessarily because of inappropriate content, but because kids simply won't understand the things the [insert form of media here] is dealing with. Kids won't find enjoyment in it, and may just leave confused and/or bored if the film's not violent or otherwise graphic.
What pieces of media do you know that would fit this mold? Media that kids (let's say the under 13 demographic) would find neither traumatizing nor enjoyable? Things that feature no epic showdowns, gunfights or those kind of setpieces that would entertain that demographic. Films like Schwarzenegger's 80's output or Robocop, or games like Duke Nukem 3D you might have played because "it's so violent!!!" don't qualify.
Two HBO shows are my prime examples: Deadwood and True Detective season 1. Both slow paced, extremely dialogue heavy series that feature very little content kids would be able to grasp. You've got a western story without cowboys or pistol duels, and a cop show almost without criminals or gunfights. When the violence happens, it's not something I'd imagine kids would go "COOOL!" at, but very ugly and sudden. Granted, I was never one of those kids that watched Schwarzenegger movies, so what do I know. Many David Fincher films like Se7en, Fight Club and The Social Network also fit this mold, the last one being perhaps the best example of what I'm talking about.