Can I play games with EA Play Pro only, without buying from Luna or EA?

I currently have an EA Play Pro subscription, which grants me access to FC 26 Ultimate Edition. I have already added the game to my library. However, when I try to play it on Amazon Luna, it still shows the “Purchase” option instead of allowing me to play.

Should I be able to play FC 26 Ultimate Edition on Amazon Luna directly with my EA Play Pro subscription, without purchasing it separately?