I finished reading the patent. Because it is a translation from French and Chinese it has some wording errors, but as patents go it is not that bad to read.
There are 3 different implementations of the patent and I don't know which one the commercial device uses. All have a large permanent magnet ring in the base and another magnet on the floating platform, both vertically magnetized . . . with opposite polarities facing each other!!!!
This makes it completely different to the Levitron, that has the two north poles facing each other, and thus repelling. I'll try to explain how it works, as far as I think I understood it.
The first "embodiment" has only those two permanent magnets. Imagine that the levitating magnet is maintained exactly in the axis of the ring magnet. When it is high above the ring magnet, its downward facing north pole will be attracted by the upward facing south pole of the ring. However, if you lower it enough along the axis, eventually it would be like trying to place two magnets parallel to each other, and it will be repelled. So there is a height at which this repulsion will compensate the weight and the system is stable in the vertical direction. Interestingly, it is also stable from flipping over (I don't have a good intuition for this, but it doesn't look implausible, either). However, it is not stable to shifts sideways. But this displacement is measured by sensors (either Hall or pressure) and pairs of electromagnets push it back to the center.
The second embodiment is similar, only that extra permanent magnets make the lower magnetic field oval, instead of circular. This stabilized it in one horizontal direction and only one pair of electromagnets is needed, instead of at least two pair in the previous implementation. By the way, Ernshaw's theorem (mentioned on the patent) makes it impossible to make the levitation stable in every direction just with permanent magnets, so this is as far as one can go.
The third embodiment is perhaps the more mysterious. Now a second ring magnet is added to the base, but with opposite polarity. This magnet has a smaller diameter and it is less powerful. In addition the magnet on the levitating base is not anymore a simple disk, but it is shaped with the addition of a pedestal (the cross section is like a T). This makes it stable in a horizontal direction, as the polarity of the lower part of the levitating base repels the same polarity of the new smaller ring. But now by Ershaw's theorem, the platform cannot be stable in the vertical direction. The patent claims that there is a metastable height at which the levitation can be maintained by sensing its speed and acceleration (with sensor coils) and providing a compensating field with an electromagnet coaxial with the others.
According to the patent, all these implementations consume very little energy. If somebody had shown me the idea before trying it, I would have bet it wouldn't work, but obviously I would have been wrong.
I guess somebody needs to get hold of one of these and disassemble it to find out which implementation was used. The first one is the one that uses more control coils while the last one the least, so that points to #3. However, the patent mentions that 1 is the most prone to maintain a permanent rotation of the base, which the product has. The way it works, a small tilt of the floating magnet (or a little extra magnet) creates a signal on the sensors that ends up producing a feedback torque if it is rotating a the correct speed.
I am still amazed that it can hold something sideways
.