Well, I watched the beginning and I think I know how I would do it.
I’d texture a cube with two shadeless blue, two shadeless red and two shadeless green sides. This means I can always do a 90 or 180 degree twist going from any one color ending at another or a 180 degree twist going from one color to another ending on the third.
For the animation I’d animate single cubes, copying and off-setting/reversing the animation for other cubes, I mean, that’s basically a choreography problem more than anything else.
The in comp I’d create the alphas. The reason I used three colors is that this allows me to create three different alpha’s by replacing one color with black and the other two with white. So I can switch between three different source videos/images or two source videos/images + white.
Lastly you need a copy of the complete scene/animation in something like AO/clay-render to use as shading multiplied on top of everything else.
And I hope you get how I mean, hehe, it would work. But, as with so much working with 3D and comping, there’s always a couple of different solutions, which is ‘better’ is the one you like and feel comfortable doing, the one you ‘get’.
Edit: Now I’m gonna check the rest of his tutorial and see how he solved it.