As an undergraduate, I had Set Theory class taught by Paul Halmos (yes, *that* Halmos).
On the first day, during his introductions, he suddenly veered into grammar. He addressed the ignorant statement as put forth in the quoted text above that "To recap: In English, there is no gender-neutral pronoun for a single person."
First noting that some languages have a pronoun for persons of unknown gender, he finished with "English is such a language. The word is 'he.' So you will forgive me if I do not say 'he or she' throughout this course."
He was (and remains) correct. "He" and "him" do not imply gender in English unless context indicates otherwise.