I can’t speak from experience as I don’t own any Amazon devices, but I have read reports that it seems to work fine with the FireTV variant of Android.
The dev has only tested it against Chromecast with Google TV, with that said I’m using it on a Shield TV and a Shield Pro and it runs fine on both.
For digital copies, they could bury this into the EULA and make it a requirement that you agree to it before you make your purchase (IIRC some storefronts do this already).
However for physical copies I suppose there could be a case made if the duration of support was not disclosed at the time of purchase (or it was not printed somewhere on the outside of the packaging).