I'm guessing but it's probably because Prime wants tostream more 4k and/or he newer Prime app is going to use new features/API that the old apple tv doesn't support.
Get a fire stick and plug it into another HDMI port. They're about 35 bucks.
https://www.amazon.com/all-new-amazon-fire-tv-stick-4k/dp/B0BP9MDCQZ/1