Update: Well the app is in the Google Play Store at this time its not allowing Android TV owners to install the app.
The Nvidia Shield already had an Amazon Video app as part of the Nvidia Shield OS. This is the first time you can find the Amazon Video app in the Google Play Store for Android TV. With this app, you can stream movies and TV shows recommended for you, including Prime Originals like The Grand Tour, The Man in the High Castle, and award-winning kids series Tumble Leaf.
From the looks of it you will only be able to stream content you already own. There is no options listed to buy new content but you can access Amazon Prime Video and content you already purchased in your Amazon video library.
Here is how they describe the app:
Prime Video gives you two ways to instantly stream Videos on your Android TV device. Buy or rent your favorite titles or join Amazon Prime and get unlimited access to award-winning Prime Originals as well as thousands of movies and TV shows at no additional cost. Browse titles, search for your favorites, or enjoy movies and shows recommended just for you. For our terms of use and usage rules, see www.amazon.com/video/terms. Amazon, the Amazon logo, and Prime Video are trademarks of Amazon.com, Inc. or its affiliates.
You can add the Amazon Prime app to your Android TV player HERE.
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