I just played through the Alpha on Ouya and a few notes:
1.) The game looks freaking awesome on a huge TV and coming from stereo speakers. My wife and I were terrified killing all the lights in the apartment. I forgot how amazing the art was for this game, so it was nice to relive it on a 60 inch plasma.
I encountered a few issues while I was playing. I'm not sure which of these are related to your game, and which are related to Ouya's Beta test of external storage.
That being said:
Earlier this week, I downloaded NN and saved it to my 64 GB USB stick I use for external storage on my Ouya. Tonight, I activated my Ouya download code to enable NN Alpha. However, I didn't have my USB flash drive in when I activated. Therefore, I was forced to re-download NN after I activated (a minor inconvience, but worth nothing).
Initially, I was playing Ouya using a PS3 dual shock controller (btw, nice touch making the on screen buttons reflect the control being used to play

However,
2.) I then switched the TV to Xbox to watch tv while I ate dinner. When I returned to Ouya, it wasn't letting me boot up the Run-Alpha of NN. I got to the screen that told me I needed to buy it, and I hit the 'X' key to purchase, but for some reason this wasn't registering anything. Instead of wrestling with Ouya, I instead tried to play the original Non-Run demo. The whole thing played perfectly without a hitch, except one small exception.
3.) At one point, I was playing and my PS3 controller shut off (battery death? I'm not sure...). I had the Ouya controller also Sync'd to the console at this point (as Player 2), and when I turned the PS3 controller back on, the game was still only accepting input from the Ouya controller (despite the fact the PS3 controller was on and Sync'd ).
Other than these issues, the game ran perfectly.
4.) Now, I tried putting my console into sleep mode and booting it back up to try to play the Run-Alpha. At this point, the game was still telling me I needed to buy Alpha, and when I hit the 'O' button to buy (mind you I've switched from the PS3 controller to the Ouya controller at this point), I was taken to a pure black screen.
So basically, I just did a hard shut-down of my Ouya and re-booted. Once I did this, I was once against asked to buy Alpha, but once I hit the 'O' button to purchase, it took me directly to the game (which was good, as I had re-deemed a code and should not need to purchase).
5.) The very first thing I did in game was begin running. I held down run and ran through the bedroom door on the Ouya controller. Only after this, the main character would never STOP running. I tried hitting R-Trigger to toggle off, but the game was forcing me to auto-run everywhere (which was quite cumbersome since I kept getting out of breath in-game :p).
I wondered if maybe this was a classic Ouya controller input issue, so I turned off the controller. When I did so, I couldn't get the controller to re-sync with the console (I personally think this was the Ouya's problem, not your games

6.) Playing through with the PS3 controller, I found that I could just hold-release-hold-release the run button to effectively have infinite run. While I didn't mind, as it was quite fun running through your haunted mansion, I think this was not as you'd intended.
7.) There were some crazy animations when I was running, like my hands would glitch and become disembodied, and the candle/axe would lag behind me as I ran, and float in the air. Maybe you were going for a Disney's Haunted Mansion like feel, but I have a feeling you're aware of these animation glitches.
Overall, the experience was awesome on Ouya, and I think it's going to be my default platform once the full version releases.
Thanks for keeping us updated Matt. If you want me to help you try anything on Ouya out, let me know. I know not many people have them, and I'm very willing to give feedback!