It wasn't Google that didn't support Amazon Prime Video, Amazon didn't add support. It was the same reason the Amazon gave for not selling the Apple TV 3rd and 4th generations. Apple worked with dozens of other providers to add apps to the 3rd gen ATV and a time could write an app for the 4th gen TV.

The proof is that there is now an Amazon Video app for the 3rd and 4th gen ATV. It was a surprise to almost everyone that Amazon/Apple ported Amazon Video to the 3rd Gen ATV after it had been discontinued for over a year.