In that video, it looks like the was duplicated multiple times and each layer was masked to create 1 piece of paper---each layer is one fold. Then the anchor points are moved to the fold line and rotate some in 3D space. Add some lights to give it some shadowing & falloff and you are done.
"I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work."
---THOMAS EDISON on inventing the light bulb.