I remember trying Adobe AIR on an Android TV, though. With a remote control, it dispatched keyboard events. I think that I mainly had to listen for up/down/left/right arrow keys, the enter key, and the back key.
When I tried Adobe AIR on Apple tvOS, I think that I had to listen for touch events, and possibly also keyboard events. I don’t recall if AIR translated the touch events to mouse events on tvOS, like it does on iOS.
In native OpenFL/Lime apps on any platform, we get our mouse/touch/keyboard input events from SDL. SDL doesn’t necessarily behave exactly the same as Adobe AIR, so my experiences above may or may not be relevant.
Well, my only experience running OpenFL content on smart TVs was through their browsers, which worked as expected. But in that case, the cursor responded to the browser, not to the exported content directly. Clicking on it worked normally.