I think you misunderstand vibrunazo's point about some games being "Ouya ready". You can already plug an Android into a TV and connect it to a controller, so some games already offer proper, non-touch gamepad support, designed to work on a big screen.

Here's a video of Sonic 4 Episode 2 that demonstrates this: http://www.youtube.com/watch?v=8fUP6mh3aOg

Plus, touchscreen games don't all require you to tap specific points on the screen (as in your Reversi example). Look at Temple Run: you duck and jump by swiping down or up, from anywhere on the screen, rather than tapping on-screen Duck and Jump buttons.