All right, so, I take it back, you can absolutely install angry birds even if you've moved the filesystem to the SD Card. I didn't realize ES File Explorer could move the apk from the external to the internal SD Card.
Did you actually get it working at that point though? Firstly, the game will crash the entire edge if you attempt to play it in portrait, you have to rotate to landscape first (simple enough) However, in either landscape mode the game has the problem of not responding to touch inputs in the right place. If I click the gear (settings) icon, the other side menu will open where I can share via facebook or watch videos. If flipped around to the other side, the opposite problem. Also, the sound, info, and background buttons then don't work.
This is 1.5.3, the latest version, also I DO have my edge flipped to have the reader on the right hand side. If anyone else feels like messing with this further, quick hint, you don't need to root or pop out your SD card, simply go into settings under "device storage" (NOT the app, under settings) and simply unmount the SD card from there.