AFAIK doesn't pyrolytic carbon need a N-S field in order to levitate? That's the one key difference I can see - this looks like the traditional superconductor trick of just levitating in a simple field.
But it still looks dependent on their being a NS pole at a corner.
That said...from this video https://sciencecast.org/casts/suc384jly50n I'm very suspicious of the behavior you see in the last few seconds where it gets pushed over to the corner and seems to fall right to the magnet That would be consistent with their being a ring magnet underneath the top magnet their, and once suitably over into the corner it loses the diamagnetic property because there's no N-S pole. The "seam" on what should be a bulk magnet in both videos that are out seems like an obvious problem.
So yeah...I think put me down for this is diamagnetism with pyrolytic carbon (the image in the paper also notably hides what you see in the video - that there's a seam on the magnet where it looks like it's a stack of two).