Am I right to read this as "the classical computer and quantum computer compete at the task of being that particular quantum computer?" Scott Aaronson is probably preparing to denounce this experiment already.
Performing such a trick demonstrates that you have a working device that can perform arbitrary quantum computations - unlike, say, the much hyped D-wave quantum annealing device.
But yes, it's basically "represent a quantum computer of this size", which we legitimately can't do classically beyond a certain size. It's not hugely useful but it's legitimate quantum supremacy, if it works.