The authors used the LIGO Scientific Collaboration's (open source) Bilby package to do the nested sampling analysis. So this was a drop-in use of this GW software to analyse the antikythera data. There is quite a close analogy between the 22-dimensional antikythera analysis, with its intrinsic and extrinsic parameters, and the ~15 dimensional spinning binary black hole analyses done in the GW world, again with intrinsic and extrinsic parameters. That's the GW connection, and it may not be so clear from the reports.

Yeah, so after collecting enough opinions from enough people, I'm 100% confident saying there isn't truly anything specific to GW here. When I use the ROOT library from CERN to analyze my molecular dynamics data, I'm not doing particle physics, I'm using ROOT as a general purpose library.

It doesn't really matter. The work is not exceptional, it doesn't shed new light on anything, and really only got the coverage it did due to clever use of key words and hype by the press release authors. In other words, like 90% of popular science.