I think your summary is not really correct, maybe I'm missing something. As far as I can read, the approximate takeaways are these:

* LLM chess play is hyper sensitive to the harness being used (see: the section on regurgitation), and only mildly sensitive to fine tuning

* The best ELOs the author was observing were from 1500 to 1750 or so (circa 2024/25). Not grandmaster, but no longer incompetent monkey either.