It kind of looks like the o-ring driving the pulley under the ball is around a fixed shaft that the rest of the mechanism rotates about. that would turn the ball a small fraction of a turn for each revolution of the tilted ball (the motion that winds a diagonal wrap of yarn) so the wraps progress around the ball.
after a closer look it may be that the o-ring is a tire that just presses against the fixed center shaft or perhaps a small ball on the end of it. in any event the shaft holding the ball at a 45* angle is turned slightly each revolution around the vertical shaft that is hollow with a fixed shaft coaxial in it
sorry for the awkward explanation: I can visualize it but am having trouble describing it.
this link has one made of Legos. I do think that the o-ring is used as a tire to drive the gray disk that turns the coil. that would correspond with the bevel gear in the lego one