The issue is that the kid wants to play a game with his friends.

So that is "online" in the sense that it uses the internet.. but it isn't the same as a web browser, or an open store of every online app.

I run game servers for my nephew. I know he only adds his friends and I can keep a loose eye on them. I don't care if his friends talk about boobs or make penis jokes (they're 14), I only care that there aren't any predators.

This is a clear and meaningful distinction and it doesn't sound supported.