@douginamug The question is, what is it most popularly known as? In the absence of some evidence that the game would be more clearly identifiable as "Bach or Stravinsky", I would leave it as is.
FWIW, the original title is stereotypical, yes, but it's not a negative stereotype (nothing wrong with ballet or boxing!) and like many stereotypes it contains a certain amount of truth.
@douginamug I don't think I've ever read the term "Bach or Stravinsky" until your post, but I doubt that proves anything. If indeed the name will change, then wait a decade and perhaps by then it will be obvious that the WP article ought to be renamed.
@mpjgregoire yeah, that's hard to tell! I turn to ngrams... 'battle of the sexes' used much outside of game theory, swamps signal.
'bach or stravinsky' vs 'prisonner's dilemma' more interesting https://books.google.com/ngrams/graph?content=bach+or+stravinsky%2Cprisonner%27s+dilemma&year_start=1800&year_end=2019&case_insensitive=on&corpus=26&smoothing=3&direct_url=t1%3B%2CBach%20or%20Stravinsky%3B%2Cc0%3B.t4%3B%2Cprisonner%20%27s%20dilemma%3B%2Cc0%3B%2Cs0%3B%3Bprisonner%20%27s%20dilemma%3B%2Cc0%3B%3BPrisonner%20%27s%20Dilemma%3B%2Cc0#t1%3B%2CBach%20or%20Stravinsky%3B%2Cc0%3B.t4%3B%2Cprisonner%20's%20dilemma%3B%2Cc0%3B%2Cs0%3B%3Bprisonner%20's%20dilemma%3B%2Cc0%3B%3BPrisonner%20's%20Dilemma%3B%2Cc0
Sure, it might have some truth... but now we're having a discussion about gender stereotypes instead of game theory 🤷 I estimate the name will change, unless game theory loses all relevance (which I hope it doesn't)