Ouya only supported selected games because games designed for a touchscreen interface are hard to play on a TV and with a gamepad. Amazon can support all games if they want to, but they're going to run into the same problem where most of them suck.
I said in another comment , but you're thinking candy crush I'm thinking emulators and titles like GTA, Modern Combat, Minecraft, and many other rpg and fps titles.
Most of the games on the play store have controller support. With a ps or xbox controller and apps for mapping if necessary.
