It's not at all a nit. If one of the dimensions did indeed correspond to gender, you might find "king" and "queen" pretty much only differed in one dimension. More generally, if these dimensions individually refer to human-meaningful concepts, you can find out what these concepts are just by looking at words that pretty much differ only along one dimension.
I'm sorry, I don't get your point at all, and have no idea what you mean by "did this". If you asked for an embedding, you would have gotten a 768 (or whatever) dimensional array right?
For word2vec I know that there's a bunch of demos that let you do the king - man + woman computation, but I don't know how you do this with modern embeddings. https://turbomaze.github.io/word2vecjson/
There’s absolutely no reason to believe that the coordinate system of the embeddings would be aligned along the directions of individual concepts, even if they were linear and one dimensional in the embedding space.
