I'm not sure why people are so eager to recommend calling the cops, especially when this kid doesn't seem to actually be causing any harm. I mean, he's being a shitty houseguest, and OP probably shouldn't their son have him over again, but going straight from "kid I'm watching is misbehaving" to "get out or I'm calling the cops" is pretty unreasonable. You agreed to watch the kid. If his parents won't pick him up early, just let him keep playing video games until it's time for them to pick him up, and never let him back in your house again.

I find it rather telling that OP doesn't mention anthing about why the kid's parents won't pick him up. Are they even home? Would the kid even be able to get into his house if he went home on his own? It's not like 11-year-olds typically have housekeys. Can the parents come pick him up? For all we know, OP could be calling them while they're waiting for a relative undergoing surgery or at a parent's funeral or something equally important.

Also, I'm kind of confused that nobody seems to have considered whether OP might have some kind of legal responsibility to look after the kid they (presumably) agreed to look after. IANAL, but I'd be surprised if there weren't some kind of law covering volunteering to look after someone else's child. I'm kind of skeptical of the assumption everyone seems to be making that you just get to declare a kid you invited over a trespasser because you don't want to look after him anymore and his parents won't pick him up early. Kids aren't adults...you can't just assume they can look after themselves if you kick them out.

And yeah, if OP calls the cops they pretty much guarantee that their son will never have friends over again. Would you let your kid go to someone's house who went nuts and called the cops because a kid was (shock of all shocks) not behaving perfectly?