Even without an official rank, on Voyager he was still considered a Department Head and (more importantly) the CMO, which gave significant authority (even exceeding the Captain on certain medical matters), regardless of whether or not he was ever given any pips. The same thing would likely apply on subsequent postings.
If he ever had to be assigned a rank for clerical/administrative purposes, it would probably be the default required rank for a Starfleet CMO candidate for the class of ship he was serving on.
No shit. Chess programs are specifically built and optimised to the nth degree for this specific use case and nothing else. They do not share the massive compute overhead and convoluted nondeterministic nature of an LLM.
This is like drag racing an F1 car and a Camry and being surprised at the result.