Reading about this mechanism will be much more worthwhile if you try it first.
Make sure motor is turned on, then turn handles facing you, one with each hand. You can slow down/stop at any position and change direction as you like.
Your right hand is turning the unbalanced weight with no assistance, so you'll feel the extra effort needed to lift the weight, and you'll notice gravity pulls it down if you let go the handle go.
Your left hand benefits from power assistance from the torque amplifier. So even though it's the same weight you're lifting, you need to apply far less force, and you'll only feel a small difference between weight going up and going down. The weight isn't able to return to lowest position if you release the handle.
That's what a Torque Amplifier does (not to be confused with Torque Convertor, which is another thing entirely). Its output will cope with quite big forces, but the force needed on its input is comparatively tiny. It also arranges that its output turns through same number of revolutions (or part revolutions) as its input. It's not perfect - there's a small amount of lost motion between input and output, and it won't accept input rotation beyond a certain speed.
So how does it work? When you turn its input, the effect is that the input worm behaves like a rack and moves its shaft slightly towards one end. This movement causes a friction clutch to engage, and the other side of the clutch is continuously driven in such a direction that it causes the worm, now behaving as a worm, to wind itself back to the mid-position where neither friction clutch is engaged. In addition to this, gears link the worm shaft to the output worm, driving the weight on the output shaft. If you turn the handle the other way, the worm moves its shaft slightly towards the other end, and causes the other friction clutch to engage. The continuously driven side of that clutch rotates in the opposite direction, so again the worm winds itself back to the middle. Remarkably, the overall effect is that the pinion on the input shaft manages to back drive the worm! Which we all know is impossible - unless as here you have power assistance.
As far as I can tell from the copied instructions page, it was Canadian enthusiast Hubert Hogle who came up with the original idea of this ingenious, subtle and compact mechanism. In my version the drives into the friction clutches are very different to Hubert's original, but the core concept remains entirely his.