The hard part about motorizing it would be the variety of angles it can be positioned in. George pointed out that it can be positioned to face straight up to the ceiling or straight back to the back wall or to either side or anywhere inbetween. This was smart on Sterns part because everyone has different gameroom setups. It also has a focus ring on it so you could get it to focus regardless of the distance to whatever wall or ceiling surface you were pointing at.
I tried to get a decent pic of it at expo and it looks like its attached via a u shaped piece that is similar to telescope mount. It can swivel around (is that yaw?) And tilt up or down (pitch?) Then you rotate the whole tube part to orient the image point straight up on the surface (roll). Once positioned i'd think you'd want it to stay there.
It would make sense though for the game to flash on or off at the appropriate times during game play.
I like that the signal image is true to one from the tv show. A lot of the car mod led door projector things you see on ebay are a generic batman logo or from the nolan batman films. I've never seen one that used the tv show version like thos one does.