I downloaded the official Prime Video app for Android TV and, for my surprise, it installed and works perfectly. All navigation in the app works perfectly by the remote.
Original Apk (unmodified):
Does not appear in "My Apps" or "Recent" lists on home screen, only in the apps menu (holding the home button).
It's the same app, but modified to appear in "My Apps" list on the home screen. It does not appear in the recent list, though.