You may have misinderstood, and I also oversimplified. The word "sex" is translated by the main online Korean-English dictionary as 성, the local pronounciation

You may have misinderstood, and I also oversimplified. The word "sex" is translated by the main online Korean-English dictionary as 성, the local pronounciation for the classical chinese character for the category of sex, or 성별, which translates back into English again as "sex". The word "gender" is also translated as 성별, and also has an entry for [grammar] 성 구분, or the grammatical difference between sexes. However the entry under "gender dysphoria" is "feeling that one's birth sex is not one's sex." So the social role idea is totally missing from the Korean-English dictionary. The Korean-only dictionary has an entry, however, for 젠더 "jendeo," which is the imported modern Western concept of gender with all its academic usages explained in detail.