Here is a brief description from the experimenter as well on what is happening in the video:

Optical illusion? No! No cords! No threads! It isn’t a perpetuum mobile! It works with a magnetic field few minutes. The spin of the gyroscope change the negatively and positively charged sides. The same principle is the wheel angular momentum experiment. Similar experiments works with globes and spheres.

Even some of the newer hoverboard companies like Hendo technologies have prototypes that work on Lenz’s law.  Their hoverboards are magnet based and use a copper base underneath to “hover” with that type of force.  See if you are ambitious and want to try this at home yourself.  It shouldn’t be hard it would just take a few items as seen in the video.

Most of the commenters btw are saying there must be magnets under the table.  I would concur as well for this to work although it is cool none the less!