To make it simpler to understand what is happening we can break it up into two things.
1. the increase in rpm as the weights come into the central zone of the described motion, is akin to the ballerina's spin speeding up as she pulls her arms in, as Steve suggested with conservation laws.
2. The act of turning the central gear into/against the torque generated to pull it in, we are simply advancing the change in diameter , effectively speeding the weights up at a smaller radius, then letting the gear off, and so having the weights back at a slightly larger radius with the same kind of velocity it had in a bit closer.
The effect is the same as pushing a swing each oscillation, at the end of the stroke. Thats why he needs to release the torque he pushed into it ( 1/4 turn or so), and it must be relaxed back to neutral to gain the momentum. We are in effect using this "counter torque through a 1/4 turn distance to impart power to the system on each cycle of the major radius.... we have a force through a distance each time we twist the handle against the weights.
How I see it anyway, we are not breaking any laws, as we are pushing power into the system each time we turn the handle... it is using up power all the while, and will degenerate without the 1/4 turn business.
......oztules