How does the Apple TV remote control my iPhone when using Airplay?
Applications can respond to the "Remote Events" from the AirPlay device. This is some kind of back-link as you described it. Developers has to respond to those events manually (unles they are using some built in classes..). For more info please check official Apple site.


  When AirPlay is in use, your media might be playing in another room from your host device. The AirPlay output device might have its own controls or respond to an Apple remote control. For the best user experience, your app should listen for and respond to remote events, such as play, pause, and fast-forward requests. Enabling remote events also allows your app to respond to the controls on headphones or earbuds that are plugged into the host device.


So your phone is "not aware" of the remote/game controller etc. It receives some events from the AirPlay.

For the allowed events please check developer site.