How can I play local multiplayer games on Apple TV
I've reached out to Vector Unit Support. Here is what they had to say:


  Currently you need any combination of up to 1 Siri remote and up to 3
  MFi gamepads. You can't use the iPhone or iPad as a second controller
  at this time.


I would note that it is possible to use an iPhone as remote, using the Apple TV Remote app, but that will go instead of the Siri remote.

I will also add that the scenario of coupling a Siri remote with an iPhone controller is possible in Crossy Road, but not using the Apple TV Remote app. Instead they've created a feature inside their iPhone app that allows the iPhone to control a player in the TV app.

And finally, it seems the answer to the limitation of two MFi game controllers has been lifted by Apple at some point after the above statement was made back in 2015.