For enabling GCController support (the Apple TV remote), I need to specify which controllers are supported in Target Settings > Capabilities > Game Controllers.
But which controller is the Apple TV remote? The gamepad? The Micro Gamepad?
Ok, I figured it out, but I'm leaving the answer up, for people who are trying to figure this out. It's the Micro Gamepad.
Here is the appropriate link to the apple docs: https://developer.apple.com/library/prerelease/tvos/documentation/General/Conceptual/AppleTV_PG/WorkingwithGameControllers.html#//apple_ref/doc/uid/TP40015241-CH18-SW1