https://play.google.com/store/apps/details?id=com.amazon.avod.thirdpartyclient&hl=en
Though on my MiBox it's buggy. Often won't show indicator of the cursor position. Playback won't last more than a minute before FC.
Edit: to clarify, the link is for general Prime Video app on Playstore. It used to say not compatible with ATV but you can push the app to an ATV now.
The link you provided is the Mobile/Tablet version of Prime Video, maybe you are talking about this version. https://play.google.com/store/apps/details?id=com.amazon.amazonvideo.livingroom