From Daring Fireball:
Why would Apple agree to this? Financially, Apple now gets a cut of some Prime Video rentals and purchases, and a recurring cut of new Prime Video subscriptions made in-app. And Apple TV users get all the benefits from the Prime Video app supporting AirPlay 2, universal search, and integration with the TV app that Apple is trying to make the default interface for watching shows and movies. Prior to this deal, Apple made nothing from Prime Video — it was a free app with no in-app purchases, and there was no way to subscribe to Prime Video through iTunes.
Everyone wins in this situation. Makes me hopeful that we’ll see other providers such as Netflix check all of the “integration” boxes eventually to make the Apple TV experience better.