The article "Anti-twister mechanism" at Wikipedia has an animation showing Dirac's theorem. The rotation axis of the cube is vertical, so it's the distinguished direction. The four belts attached to the cube in the other directions (2 per direction, on opposite sides) move in a plausible way, allowing to intuitively grasp the result.
However, the two vertical belts seem problematic. I'll concentrate on the one coming from the bottom and attached to the upper face because the lower face of the cube is permanently occluded. Although sometimes also occluded by other belts, the attachment of the considered belt looks impossible to remain fixed. This belt, unlike the lateral ones, doesn't go around different sides of the cube every other turn. And both sides, blue and yellow, of the belt become visible twice as its most bent part goes around the cube. I believe the belt twists at half the speed of the cube's rotation. Which is impossible with fixed attachment. Right?