If you think about it, it doesn't matter which point of view it works on, if the thing is an actual circle that's interesting on its own, or presumably a sphere(?) but they don't even touch on that because "3D is hard"? Anyway, for some reason they implicitly choose our point of view as the "interesting one", funny (/s, actually lame and sad) to see the geocentric model is still alive after two millennia!
They also didn't check if other stars would form circles from any arbitrary point of view (how many circles are actually up there, not just the apparent ones), which would be a trivial calculation, but I guess "matrix transformations are hard" as well?
The whole paper is pretty weak. They calculate the "thickness" of this "circle", i.e. the distance from the galaxy closest to us to the galaxy further from us if you undo the projection; and they come up with a value of ~400 Megaparsecs. Now, you may be inclined to think "yeah, but the universe is HUGE and on that scale they may be kind of tighly packed?". Nope! It's on the order of the largest (actual) cosmological structures that we have identified, so, pretty much, they are as further away as they can be from each other, lol.
This is pretty much astrology.
Source: I read the paper.