But the abstract of the pre-print (https://arxiv.org/abs/2210.10255) covers some of what you are asking:
"Despite the well developed mathematical description of non-Abelian anyons and numerous theoretical proposals, the experimental observation of their exchange statistics has remained elusive for decades. Controllable many-body quantum states generated on quantum processors offer another path for exploring these fundamental phenomena. While efforts on conventional solid-state platforms typically involve Hamiltonian dynamics of quasi-particles, superconducting quantum processors allow for directly manipulating the many-body wavefunction via unitary gates."
They created a collection of quasi-particles that has different statistical properties that we don't see in 3D (the Non-abelian anyon https://en.wikipedia.org/wiki/Anyon). So simulated or created becomes a tricky word here, the quantum processor is putting these qubits into a state that acts as a quasi-particle so they can study it directly. So no a classical computer would not be able to do this in the same way it would have to use classical bits to simulate the quasi-particle.