The point here is that the quantum computer component of the original solution is not doing anything - that the algorithm being run overall is not actually a quantum algorithm, but a classical probabilistic algorithm.

If the quantum computer were a key component of the solution, replacing it with an RNG would have either no longer yielded the right result, or at least would have taken longer to converge to the right result. Instead, the author shows that it runs exactly the same, proving all of the relevant logic was in the classical side and the QC was only contributing noise.