Amazon doesn't support the current Apple TV or Google's Chromecast, so I doubt they'll support the new Apple TV either. Maybe they think this is an effective way to get people to buy a Fire TV or Fire TV Stick.
Sony made the mistake of getting into content decades ago. Their aim was to deliver content to their device businesses, but it made them the enemy instead of an ally of every other music, TV and film company on the planet. Apple had an exclusive with HBO Go last year. That would never have happened if Apple had their own TV service.
> Amazon doesn't support the current Apple TV
Not directly, but last I checked I could beam video from the Amazon store from my iPhone to my Apple TV.