Hmmm... a bit hard to describe since I haven't actually done any sketches for it except on paper.
Basically, it's sort of like the spool that fishing line comes on, except inside-out (ie: a 'conveyor belt' made of channel material with the open side in, configured similar to the 'hoop' in the video). It opens like a bracelet to insert the toroid, then is closed.
A 'slider' is then threaded onto the free end of the wire from the original spool and snapped into a track in the channel to maintain tension and prevent tangles. That's the part that's giving me fits right now. I haven't been able to find anything lying around that meets the requirements. Right now, all that I can come up with is to use a mandrel-bent tube and grind the inside part off to create the channel.
The end of the wire is then taped to the inside of the channel, and the channel spun up to load it with as much as it will hold.
Anyhow, once it's ready, you do a couple of winds by hand to start it off, then run the motor in reverse to unwind the wire onto the toroid.
A slow gear train, ratchet, or stepper motor increments the orientation of the toroid each time a turn is completed. I haven't spent any thought on that yet, since it's the easiest part.
As you can see, I'm nowhere near a workable design yet.