Amazon have stopped selling Apple TV on their site, if you search for it you won't find it and if you Google, "Amazon Apple TV" any links that are shown are dead ends.
If you follow tech news you'll have seen that Amazon stopped selling Apple TV and Chromecast, their two main rival streaming platforms. You can read more on this from early October, here on the Verge.
Apple have publicly said that they welcome "one and all" to develop apps for the new Apple TV but with Amazon pushing their own Fire TV Stick and Fire TV box they are simply not supporting other platforms as they feel their streaming service can fuel sales of their own hardware. Fair enough, that's their decision.
However anyone blaming Apple for the lack of an Amazon streaming app is wrong, it's nothing to do with Apple. This is entirely Amazon's doing.
There has to be a lot more to this than we are aware off. Amazon is a successful business and will be looking to increase their profit at all times. If they provided an app on the Apple TV this will make their service available to an increase group of users and be good for them. However, the fact that they have not provided one and seem reluctant to provide one suggest to me that they have not been able to negotiate an agreement with Apple that is acceptable to them.
Of course Apple will say that anyone is free to provide an app on the store and I am sure this is mostly true. However, Netflix is Amazon competitor in this space and I am sure if they were given the same terms as Netflix they would develop an app.
This will surely be worked out in time but I rather suspect it is Apple that is going to have to make the compromise on whatever it is that is preventing Amazon from moving forward.