I have done this a few times, and used pretty much the same techniques to get the glare out. Of course it took sometimes an hour per photo.
I just downloaded the app and tried it. It works pretty well. Not quite as amazing as the video nor quite as simple. Still after a half dozen shots you figure it out. The results ran anywhere from acceptable to great. It works much better if you can light up the photo so the phone flash is not needed. The second thing to know is when you move the phone to get the 4 dot views in the corner, it works much, much better if you are careful to keep the phone the same distance from the photo and even more important parallel to the photo for all four points. You also can adjust the corners and cropping afterwards.
So considering you could get good ambient light, a flat surface and knock out 3 or 4 of these per minute with glare handled, not too shabby. Now it also works nicely for highly resolved document scanning.