That’s the correct interpretation of that use of the word, and the quote in the post is meaning to use it in that way before pretending it’s a gotcha.

The term man (from Proto-Germanic *mann- “person”) and words derived from it can designate any or even all of the human race regardless of their sex or age. In traditional usage, man (without an article) itself refers to the species or to humanity (mankind) as a whole.

https://en.m.wikipedia.org/wiki/Man_(word)