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.
I'm Not an engineer, but I play one on TV. My handle is Tweety but I have nothing to do with the organization of similar name. I just had a really big head as a child so folks called me tweety bird.