Yeah, that has been the definition of it in the past. It has been re-defined by the wokeists for the nebulous concept of gender identity, but I've never seen any of them give a coherent explanation of what it is.
Merriam Webster explains;
"Are gender and sex the same? Usage Guide
The words sex and gender have a long and intertwined history. In the 15th century gender expanded from its use as a term for a grammatical subclass to join sex in referring to either of the two primary biological forms of a species, a meaning sex has had since the 14th century; phrases like "the male sex" and "the female gender" are both grounded in uses established for more than five centuries. In the 20th century sex and gender each acquired new uses. Sex developed its "sexual intercourse" meaning in the early part of the century (now its more common meaning), and a few decades later gender gained a meaning referring to the behavioral, cultural, or psychological traits typically associated with one sex, as in "gender roles." Later in the century, gender also came to have application in two closely related compound terms: gender identity refers to a person's internal sense of being male, female, some combination of male and female, or neither male nor female; gender expression refers to the physical and behavioral manifestations of one's gender identity. By the end of the century gender by itself was being used as a synonym of gender identity.
Among those who study gender and sexuality, a clear delineation between sex and gender is typically prescribed, with sex as the preferred term for biological forms, and gender limited to its meanings involving behavioral, cultural, and psychological traits. In this dichotomy, the terms male and female relate only to biological forms (sex), while the terms masculine/masculinity, feminine/femininity, woman/girl, and man/boy relate only to psychological and sociocultural traits (gender). This delineation also tends to be observed in technical and medical contexts, with the term sex referring to biological forms in such phrases as sex hormones, sex organs, and biological sex. But in nonmedical and nontechnical contexts, there is no clear delineation, and the status of the words remains complicated. Often when comparisons explicitly between male and female people are made, we see the term gender employed, with that term dominating in such collocations as gender differences, gender gap, gender equality, gender bias, and gender relations. It is likely that gender is applied in such contexts because of its psychological and sociocultural meanings, the word's duality making it dually useful. The fact remains that it is often applied in such cases against the prescribed use.
Usage of sex and gender is by no means settled. For example, while discrimination was far more often paired with sex from the 1960s through the 20th century and into the 21st, the phrase gender discrimination has been steadily increasing in use since the 1980s and is on track to become the dominant collocation. Currently both terms are sometimes employed with their intended synonymy made explicit: sex/gender discrimination, gender (sex) discrimination."
https://www.merriam-webster.com/dictionary/gender
It's this "internal sense of being male or female" which I want people who have this feeling to explain.