It’s simply worm gears which easily work this way in that three of them will mesh and turn properly. But I cannot think of any machinery that actually uses more than two meshed worm gears for any reason.

Yes, same gears, but a supercharger only uses two of them which does not seem “impossible”. Only when you put three worm gears together do you get a mind-bending demo.

That is only a restriction of flat spur gears, the tradition circular flat gear with teeth. Worm gears with that spiral along a cylinder can easily be grouped and run in set of three.

Nothing to do with gaps, the gears are all in triangular sets of three, any gears not in those sets wouldn’t touch anyway. The “magic” is from using worm gears, which allow three gears to mesh and turn freely. If people are using the mindset of flat “spur” gears (ordinary type) then three gears meshing and turning…

Only impossible if you’re using spur gears which these are not. Worm gears can mesh three gears successfully.

You have described the issue with flat, also known as spur gears. They cannot mesh in two different rotations simultaneouly such as when three gears are meshed.