The piece of paper tells the app the position of the animation and is removed by the app from the video in the iPad. If you look closely you'll see the app projects some kind of wooden surface where the piece of paper was, this could be a pattern recognition thing (looking at the surrounding pattern and filling in the paper with that pattern) or just a custom job.

I believe that in augmented reality programs you need a target. The piece of paper is that target. It allows for the AR program to know where to place the video and also how to rotate the camera as he is walking around to the side.

Ya it looks like the "augmented reality" part was faked. The angle of the video never quite matched up with where he was holding it either. In any case it's still a nice proof of concept.