It's well known that Amazon refuses to put their Amazon Video app on the Google Play store and, while they do have an Android TV version of the app, they only offer it as a pre-installed app on certain devices, such as Sony Bravia smart TVs running Android TV.
The APK for the app on Sony TVs can be sideloaded on the Nvidia Shield TV and it works, offering up to 1080p HD video (but, for some reason, no DD 5.1 surround sound). The same APK does not work, however, on the Nexus Player. Some thought that the reason for this is because the Nvidia Shield TV, like Sony TVs, uses an ARM-based processor while the Nexus Player does not.
But now we know, based on more than one report, that this same APK does not work on the new Mi Box either, despite the fact that the Mi Box does have an ARM-based processor. While the app can be sideloaded and it will launch, any attempt to actually play a video in the app on the Mi Box fails with an error message.
Any idea, from a technical perspective, why this app works on the Nvidia Shield TV but no other Android TV box? Perhaps it isn't a technical problem at all -- maybe Amazon is allowing the app to run on the Shield TV but not these other devices. If that's the case, why? There were rumors floating around earlier this year that Nvidia was working on officially obtaining the app from Amazon. Hopefully that's a development we see with the likely upcoming announcement of a refreshed Nvidia Shield TV.
I think Nvidia is working with Amazon personally.