"Take John Watson's second volume of 'Mastering the Chess Openings' – over 300 pages of theory, and the words 'she, her, hers, and herself' do not seem to appear ONE SINGLE TIME while their male counterparts appear many hundreds if not thousands of times."
Unless he's referring to a specific female it would be incorrect. It's very annoying whenever "she" is used as a general pronoun.
When I was a child at junior school, we were taught in English classes that, where the gender of the subject was not determined, the male "he, him or his" was correct. Isn't it typical of today's politically correct attitudes to complain about this age old linguistic device?
Oh please. When I was in school, we used a Latin textbook from the 50s, with a number of sexist scenarios, such as a master being pleased with the allure of his female servant.
On the point of grammar, it sounds like you grew up in an era where you were rapped on the knuckles for splitting infinitives, which most grammarians nowadays recognise as a bogus rule. Similarly, a number of style guides no longer advocate for a generic 'he'.
"To boldly go where no man (not woman) has gone before." You're right - split infinitives have always been a no-no for me! But seriously, is it not easier and quicker to default to "he" rather than "he or she" and all the rest?