

This is a pretty difficult question to answer since all phenomena are quantum. A star is powered by nuclear (quantum) fusion. Permanent magnets depend on the quantized angular momentum of electrons. Could these phenomena be allowed by something other than quantum mechanics? Maybe. But a constant goal of science is to find the simplest explanation for all we observe, meaning that whatever alternative explanations you come up with, should they be correct, then taking them all together will constitute a theory that at least looks an awful lot like matter waves (mathematically, at least).
The original paper is called “Excitons in the fractional quantum Hall effect”
If you know what that means, it’s more clear and less misleading than the phys.org headline.
If you don’t know what that means, it’s a novel combination of two known properties of materials—excitons and the fqhe.
The buzz appears to be that it leads to some weird excitations/quasiparticles that have non-bosonic statistics. Namely, anyons and fermionic excitations can appear (the former is a known phenomenon, but the latter has only been theorized—a fact that honestly surprised me). This loosely relates to some types of quantum computers, but in all honesty, I would expect this paper to only be interesting to those in condensed matter physics, and I’m not entirely sure why it was picked up and turned into a thing.