I'm pretty sure some "apps" in AppleTV treat swipes on the remote differently than they treat the "arrow" button presses from an older Apple remote and control systems.

While most apps don't care how you input a directional command, I suspect your cycling app only recognizes the swipe... I'd prove this hypotheses by trying to control the app with an older apple remote's arrow buttons. If it responds to the apple remote's arrows then you have some hope of making your control system work. IF not I think your SOL.