But don't they offer Amazon Prime on Roku?
Yes they do. But the Roku has been around longer than (the 3rd-party app capable iteration of) the Apple TV.
The Roku has been around since before the Amazon Fire TV debuted. They're not
withdrawing support from the Roku, just as they're not pulling the
Amazon Instant Video app from iOS - because in taking either of those steps, it would be hard not to be seen as the bad guy (and iOS itself doesn't compete with the Fire TV, just with their Fire tablets and phones, and the average consumer is not going to work out AirPlaying from Amazon's iOS app to the Apple TV). In fact, in the past, they've provided
Amazon Instant Video for a ton of different devices. But not only have they not made an Apple TV app,
they've stopped selling the Apple TV and Google Chromecast, and their stated reason? "Amazon is citing compatibility with its Prime Video streaming service, which is not available on devices from Google and Apple." If Amazon simply chose not to offer the Apple TV direct from Amazon, it'd be one thing, but forbidding 3rd-party sellers from selling it is quite another. That's not simply choosing not to help a competitor, that's trying to hurt the competition. But they know that if they didn't sell the Apple TV themselves
without forbidding "marketplace" sellers from selling it, it'd do well, and then it would appear in their "top electronic devices" sales lists, and would get review scores that could be compared on amazon.com against Fire TV scores, and Amazon doesn't want Fire TV to have to compete like that. (I actually have a Fire TV, from a Black Friday sale - I rarely use it, even though it's hooked up, because the interface is so clunky, and it freely intermixes content you already own or have free access to, with buttons to purchase new things - nowhere near as nice an experience as the Apple TV.)
It's very politician-y - they don't step up and say "we're getting rid of the Apple TV to make our Fire TV more attractive" (which would be understandable but make them look bad), they choose not to port to their iOS app to the Apple TV - despite their "watch anywhere" message and the long list of devices they've put their service on - and then claim the lack of their service there is why they won't sell the devices, as if it's
someone else's failing, rather than a deliberate, calculated, move on their part.
There's really only two possible explanations for Amazon's behavior in this: 1) they want to hurt Apple TV sales in order to promote the Amazon Fire TV in its place (rather than having it compete on its own merits), or 2) they want to put pressure on Apple to get more favorable terms for the situation where someone subscribes to Amazon Prime video via an Apple TV. (These two explanations are not mutually exclusive.) The first paints Amazon in unfavorable light, given that they want to be everybody's favorite store for everything. The second is particularly galling given that there's no need to give Apple any money whatsoever - simply don't offer a subscription option in the app. I use the Kindle app on my iPhone and iPad all the time, but I don't spend any money in the app (you can't), it's simply a target/output device for books I buy on the Amazon website - I buy books from Amazon
because I can't read them on my iPhone. The Apple TV could be used in exactly the same way. If I could watch movies that Amazon sells, on my Apple TV, I'd be much more likely to buy movies from Amazon. As it stands now? There's no way I'll buy video from Amazon.
It's all very frustrating - I've had Amazon Prime for many years, I like Amazon, this is ... bad behavior on their part.
Anyway, Playstation Vue looks quite interesting, in part because it apparently offers login access to lots of the individual TV network's apps, which I dropped when I "cut the cord" last spring. Might be an attractive alternative to Hulu, especially in conjunction with Apple's new "TV" app, if that works out well.