What I can highly recommend is the (free) RetroArch app for AppleTV. You upload your legally owned ROM files via a simple web interface and you can just pair your bluetooth gamepad with the AppleTV.

Side node: The same thing works on phones, too. While most of the games are not very fun on a touch screen, I've found that turn based games like RPGs hold up remarkably well.

edit: I'm referring to AppleTV the box, not the service

What happens if you upload illegally owned ROMs, does Retroarch has some verification on Apple TV? Never noticed it when playing on Android TV or PS3, so the words "your legally owned" seem redundant.