For any allegedly-random distribution, it's possible to statistically determine an upper-limit on the size of non-random-appearing structures. The upper limit for such structures in our universe is thought to be about 370 MPc, about 1/3rd of the size of this ring.
I’m guessing the point is something along the lines of, if you have a page of randomly-distributed points, you would expect to see small features but a large circle spanning the page would be inexplicable.
That makes sense, thanks for actually explaining the core idea.
A lot of these questions are much more clearly addressed in the previous paper by the same authors, which is much more layperson-friendly: https://academic.oup.com/mnras/article/516/2/1557/6657809?lo...