http://www.androidpolice.com/2015/05/16/amazon-disables-the-...
Netflix, Hulu, HBO, Crunchyroll, etc. all support Chromecast. It would be extremely easy for Amazon to support it, if they wanted to.
> But now it doesn't work. "License Error" codes have started showing up when running the Instant Video app on the Nexus Player, presumably because someone at Amazon saw that it was running on non-blessed hardware and shut it down.
> Amazon’s streaming service, called Prime Video, doesn’t run easily on its rival’s hardware.
So it does run, at least according to the article. But it's either hard to make it run, or it doesn't work well. Both of those seem to contradict your link. Very puzzling, I guess one of those must be wrong?
There are no technical or legal barriers preventing Amazon from supporting iOS and Android devices.
I don't think you can say Apple is to blame (or Google, though the google situation I can't speak as clearly to because I don't know the technical details there.)
On Android, it's Google Play Services, while on iOS it's a custom Cast binary that Google provides to developers to link in their apps. Due to this, almost all apps that support Cast are on iOS, Android, or Chrome because closed-source binaries are only distributed for those platforms.
Amazon would have to make special arrangements to include the Cast SDK on Fire OS. I still don't think this excuses them from bringing a proper Amazon Prime Video app with Cast support to iOS and (Google's) Android.
Overall the article just says Prime "doesn't work well" on those devices, but does work well on others. It doesn't say why. At this point it's hard to say who's to blame. It would have been nice if the article had investigated the issue.