This is vertex animation. As in Cloth or maybe even liquid. It's done with morph targets - just like the facial animations. Only here it is used for playing a continuous cloth animation. It won't play in Editor or Game only with special tricks or by setting up the morph targets in Facial Editor - but it's not smooth.
EDIT : I was requested by PM to send the scene with the cloth - and from another user a regular scene with just a box and a plane as a cloth sim. SInce the attachments limit in PM is 20 KB I placed those files here.
a short info for each file (I used 3ds max
cloth-sim-w-boxes.rar : first I simulated a plane with Cloth . Then I placed a box at each vertex. I baked the boxes animations, applied a skin and chose the boxes as bones. Since the sandbox takes I think maximum approx 170 bones I split the plane cloth in two. And then saved as CHR obj and CAF anim
cloth-sim.rar - and cloth-sim-higher-quality.part#.rar - just a simple box and plane with cloth