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This doesn't have anything to do with magnetostatics as far as I can tell. This is an effect of gravity. The spinning magnets tilt towards earths gravity (down) and put more friction between the surface there, meaning more force on the bottom half of each part of the rotation at the glass/magnet interface, causing it to move right when spun clockwise and left when spun counterclockwise. Just like a wheel.

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I was starting to think my solution was way too simple to be correct, but I believe this is the correct answer.

As the magnet starts to fall towards the earth due to decreased friction, there begins an inbalance in the friction between the lower and upper contact points of the spinning metal upon the glass. The lower part of the glass becomes an area of increased friction due to both the shape of the magnet and the fact that the friction created by the magnet moving downwards affects the bottom part of the spinning metal most.

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This last bit is why I was going on about velocity-dependent friction in the other thread. I'm not sure what the argument for increased friction on the lower side is if you don't have such a thing. However, the argument that the shape isn't flat and will lead to tilting downward would mean greater pressure there and thus more friction seems solid. And you're right that if there were more friction on the bottom side, then it would have this effect.

I'm with the people that say that the magnetism is probably a red herring here. I think the only reason it is necessary is to give you something that will keep the frictional force for you. A pretty quick experiment that should address these concerns: take a pane of glass, and lay it parallel to the floor. Set up your magnets on that system and spin them. Without the gravitational asymmetry, by these arguments they shouldn't have the same left-right behavior. (I think the actual dynamics will be complicated because of coupling between different axes of rotation from the weird shape. That is, spinning it will lead to pitching and rolling on the other axes.)

EDIT: For that matter, spinning one of these things by itself on a flat surface should do the trick for debunking the magnetic claims, I think. I think the key thing here is that if it were the magnetic fields, the force wouldn't always be to the right, as the whole thing should be rotationally invariant, and would always be to wherever the "right" is right now.