It is well known that Amazon and Google have a high rivalry. The fact that the Amazon Music App has begun to support Chromecast was a surprise, something nobody could have predicted.
Rivalry has increased when Amazon, the massive online retailer, consistently removed a number of Google products from their site. One reason for this move was that Google Home and Chromecasts are in direct conflict with Amazon Echo and Fire TV devices.
However, at the start of the month, TechHive wrote an article about Amazon testing Chromecast support for Amazon Music App, but at the time it was only for some devices. After two weeks all was made official.
As can be seen, Amazon’s intentions are not quite clearly, but maybe in the future they’ll bring Chromecast support to the Prime Movies App too. Hopefully you’ll give it a try.