This is definitely very cool, but "reveals" is a strong word. They've demonstrated that it's a plausible explanation for the puzzling distribution of stars in this cluster, but there are still other explanations that have not been ruled out.
What's puzzling about the cluster is that the stars appear well-mixed -- the high mass stars follow the same distribution as the lower mass stars. That's weird because globular clusters should undergo mass segregation, where the high mass stars slowly congregate towards the center while the lower-mass stars migrate towards the outside (interestingly, this is because self-gravitating systems have negative heat capacity, which is a concept that tends to freak out non-astronomers). And we indeed see that most clusters are mass-segregated.
So why do black holes help? They form from the most massive stars, which died early, and they end up being significantly more massive than the lower-mass stars that are left. So if there are lots of black holes, then the effect of mass segregation is to make the *black holes* congregate towards the center. In other words, mass segregation is still happening, but it's operating on black holes (which we can't see, so we don't notice its effect) instead of stars (which we can see).
There are other ways you can explain this, though. If there's a massive-enough intermediate-mass black hole at the cluster center, that makes the process of mass segregation take longer, so it might not have had time to make any significant change. A sufficiently large fraction of binary stars within the cluster could have a similar effect (i.e. make the mass segregation timescale much longer). Or, more speculatively, you could posit that there was some dynamical event that happened to the cluster since its formation that mixed the stars, so mass segregation has not had as long to operate as we assume. So their explanation is a plausible interesting one that they have demonstrated can indeed cause the desired effect, which is really cool! But these other options also need to be investigated.