The paper shows a clear phase transition to diamagnetism as the material is cooled. That would be seen in superconductors and not in regular diamagnetic materials. I'm not aware of any that have that kind of phase transition. Though since we're in weird territory here, it's important to note some weird non-superconductor behavior that's beyond regular diamagnetism might be going on as an alternative explanation. But it is weird.
ETA: also, in the presence of a magnetic field, that transition temperature decreases. That's pretty huge. Unless this paper is fraudulent, I take this as the biggest positive evidence so far that something besides simple diamagnetism is going on. And, cards on table, with the assumption that the paper is not fraudulent, this pushes my odds above 50% for the first time.