It is clearly resting on the magnet. I don't know the mechanics off the top of my head, but that is enough mechanical constraint for a pair of permanent magnets to levitate.
Reminder that flux-pinned levitation only occurs when superconductors are cooled from above to below their critical temperature while in a local magnetic field.
The researchers probably didn’t heat up their big sample above the critical temperature in air as that could have mechanically destroyed it. It was already chipped almost in two.
Casual demonstrations of levitating superconductors involve first submerging the superconducting material in a (non-magnetized) tub of LN2, and then moving it onto a magnetic track. For example, https://www.youtube.com/watch?v=X5EoUD-BIss