From my understanding, gender is a social construct belonging to the concept of Superstructure and as such it can be influenced.
Gender is more than that. Just like relations to the means of production in a capitalist society form a class system of capitalists and the proletariat, relations to the means of reproduction in pretty much any society form the class system which we call gender. Reactionary and revisionist thought capitulates to this class system and champions "sex" as the material reality from which gender arises but Marxian analysis must see the relations to the means of reproduction as the basis, the classes of "sex" as the superstructure, and the idea of gender as an all-encompassing term for the basis and the superstructure. The statement in the OP is reactionary and revisionist.
I hope other comrades provide links to more literature, this short read is a good intro to modern thought on gender unburdened by capitulating to the reactionary.
Помогите, империя зла заставляет меня говорить на искуственном языке!
P.S. Using the word "horde" in this context isn't racist since this word comes to English from the word Turkic tribes used to describe several concepts related to their statehood, i.e., the horde is just what they called themselves. In fact, the word is still actively used by the descendant Turkic states, e.g., the residence of the president of Kazakhstan is referred to as Ak Orda – white horde. What is racist is all the negative connotations and associations this word acquired once adopted to English.