I watched the video and the speaker's hand movements show exactly what he meant (which isn't necessarily what other people would mean by the same words). The speaker moved both of his hands horizontally while he said "across" and raised one vertically when he said "up". He also moved them horizontally when he talked about men choosing women "across" hierarchies and lowered one when he talked about men choosing women "down" hierarchies. This means that the term "across" when referring to both genders means, for the speaker, "choosing partners of similar status".
As I said I don't believe that everyone would use "across" in this way but the speaker in the video obviously did because his gestures agree with that interpretation.
I also don't agree with his suggestion that no man chooses a woman of higher status and that no woman chooses a man of lower status; there is a bias in those directions but it is not universally true. Both Queen Victoria and the then Princess Elizabeth married men of lower social status (and their husbands married women of higher social status of course). It is also true that there have been many marriages of ordinary people which broke his "rule" many of which have been as successful and long lasting as the royal marriages mentioned above. To my mind he has damaged his case by saying what is provably incorrect when he could have made a strong case by inserting "usually" or "have a strong tendency to" into his argument.