One main advantage that immediately comes to mind - the rotation is freed of gimbal lock in otherwise nested systems of rotation. Aside from the strain of keeping low temperatures, the future is looking good.
Unfortunately, the video's description - as is all too common - makes an erroneous claim which propagates misconceptions: "seeming to defy the laws of physics."
First of all, events which seem more common than others - even with relentless success - cannot be proven to be laws a priori without already being axiomatically grounded. A true law cannot be broken. What was/is/will be a law of physics, however, is that this sort of levitation was always possible, still is, and always will be, regardless of your awareness or ignorance thereof. Absence of evidence is not evidence of necessary absence. One cannot deduce impossibility from mere inactuality. Vice-versa, yes. If something is impossible, it is necessarily inactual.
Most see my stoic approach as lacking appreciation for the marvelous - an accusation I vehemently refute. That the most banal and common of phenomena could even occur has, to me, marvel which rivals even the rarest phenomena. On a basis of the fundamental, recursive "why?" - both are as unjustified as each other. Yet still they can occur at all.
So to my naysayers - no. I do not lack appreciation. My appreciation far outweighs yours. It is the sort of appreciation that admits both the true laws of logical rigour and the freedoms of physics that you yourself would have otherwise bound by statistics - not laws - and thus denied by an ever premature conclusion that those phenomena were "impossible".
Enjoy the video.