Those of you with backgrounds in materials science, ceramics engineering or graduate-level physics may recognize this phenomenon as something similar to the
Meissner-Ochsenfeld effect, though strictly speaking what you're witnessing is
not a result of the Meissner effect.
In the Meissner effect, the superconductor that is placed within the magnetic field deflects the field entirely (see the image pictured here), such that none of the field passes through the object itself. But as Hanson points out, the thinness of the superconductive coating featured in the quantum locking video allows for the magnetic field to penetrate it (albeit in discrete quantities) wherever there exist defects in the superconductor's molecular structure. This penetration gives rise to the "flux tubes" (again, pictured alongside Hanson's explanation), which pass through the inert crystal sapphire wafer and "trap" it in midair. This trapping provides the
typically wobbly "levitation" characteristic of the Meissner effect a stiffer quality.