How I understand it: the "computation" is actually "sampling" the cubits? And then sampling results in the sets of random numbers, which don't have uniform but some specific distribution (specific for quantum effects). Then they claim that such a distribution could not be achieved using classical computer so fast, if the classical computer has to do the simulation of the cubits. And therefore, they claim that their quantum process is better.
But couldn't one do a similar conceptual setup even before, e.g. measuring some noise source (e.g. a semiconductor based diode etc) and then claiming that measuring the source is faster than simulating on the digital computer the analog behavior of the noise source?
The interesting step here is that the source is not a single element but a set of quantum qubits, which is much harder to simulate, but on another side it appears that dealing with the behavior that doesn't allow e.g. Shor algorithm on the same setup is avoided by decision to do what was done.
Seems like a clever trick, but I miss in which aspects it makes the hoped-for outcome (e.g. breaking some crypto keys using Shor) in any way more achievable than before.
Please don't assume that I really know what I write, but consider this as a possibility to explain to the not fully informed public which however shows an interest in the topic.