That is actually a very good definition of "gender", as that term is used today. Problems arise when SJWs of various stripes conflate (whether deliberately, or out of ignorance) "sex" with "gender". Gender can indeed be "fluid", since it's just a made-up construct. Sex is binary and fixed, because it's rooted in biology.
If we insist on using the right terms, we wouldn't have (e.g.) insane public bathroom policies. There are many very good reasons for segregating the sexes, in many places -- OTOH, it's pointless to try to segregate the "genders".
The loony left knows the power of controlling the language. Don't let them away with it. Insist on using the right terms: "sex" for biology; "gender" for all the made-up stuff.
“The loony left knows the power of controlling the language.”
Yep! It’s why they prefer to use the term “Democracy” when describing the USA and not “Republic”.