The Final Fantasy III remake port (as in III by the japanese numbering, not american III which was VI) has been out for awhile already on Android. It really works pretty decently for being on a phone/tablet, I recommend checking it out if you can stomach $15.99:

https://play.google.com/store/apps/details?id=com.square_eni...

The game is a port of the DS remake to begin with, I doubt "coming to Ouya" is much more work than maybe adding controller support to the Android build.

It looks like SquareEnix just released FFI also.