I once hired a teaching assistant for a class based solely on the fact that the applicant was previously the president of his college go club. Someone with a good go+math background would be near the top of my wishlist for research assistants.
That said, I don't think that mentioning that you were a go teacher in the work experience section is a good idea. You should definitely mention go at the end of the resume though. I've seen a small but significant number of resumes that mention the applicants' chess skills in the miscellaneous section. These resumes usually mention that titles (FM/IM), rating, and tournament wins. The idea is that many people in the western world believe chess skill to be a good signal of high intellect.
I would suggest that you do something similar that frames your go skills as being comparable to having great chess skills. Keep it as brief and clean as possible
E.g.:
Notable Miscellany
Player/Teacher of Go (Chinese chess, also known as Baduk or Weiqi)
Achieved the highest rank recognized by the American Go Association (rough equivalent of chess title XM, estimated Elo ~xxxx)
Tournaments wins: A, B, C
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This removes the 6th dan (which is just confusing for anyone who doesn't understand Go). The "top 200 player" bit may be lead to some dismissive undervaluation given that the number of Go players in the US may be perceived as being very low. "Studied professionally" does not make any sense unless you were making money by studying go. Mentioning that a professional player was your teacher is probably a bad idea. The general perception is that most teachers are professionals (whether the subject is piano/golf/tennis/whatever). Since most people do not understand that becoming a Go professional is like becoming an NBA player (in the sense that the minimal bar for entry is ridiculous), most people will believe that you are just padding lines on your resume. Yes, I understand that go is not Chinese chess, but it is just about briefest way to get your message across.
I'd be happy to talk more if you PM me, but that's about the gist of my advice.