First it shows a temperature graph vs moment, as they heat it it loses the diamagnetism around the temperature LK99 is said to be superconducting.

Second only a superconductor will have net-zero field, which means "stable" levitation. In the video they approach the sample with the magnet and flip it while the piece is mostly "in place". A regular diamagnet generates a external field that "follows" the field applied so it would likely move sideways, that is why to "levitate in place" a diamagnet people normally use a Halbach array.

EDIT: A Halback array is made alternating the poles N-S of the magnet, so that forces of repulsion created by the diamagnet cancel. This is why you will see people using multiple magnets when levitating pyrolytic graphite.