I do this regularly for my mom now, since we saw the video. She will buy a bunch of fresh garlic, then have me peel it in bulk for her. Then she just keeps that in a jar in the fridge for when she's ready to use it. Another nice thing about this method is you only have to make a mess once with all those garlic skins. That's one of the things I hate about peeling garlic is that those paper-y skins get all over the place and keep falling all over the floor.
One caveat though I've noticed when trying to use this method - you need garlic that has dried out a bit first, to the point where the skin is brittle enough to break off easily. I've tried doing it with fresh garlic that has been pulled from the ground, and it didn't really work well, and ended up bruising the garlic. Also, you can only do so many cloves at a time, otherwise the skins start to pad the other cloves which have not peeled yet, and soften the blow, so they end up not peeling. You may periodically need to remove some of the excess skins as you're doing it.