The Seanchan don't seem to do this that I recall. Tylee and Egeanin don't seem to be looked at as men. The Seanchan just seem to rigidly stick to their caste system with no regard to male/female beyond the normal interplay.
Yeah, they take it to a whole other degree that the gender issues don't come into play so much.
IDK, part of the bit about being aristocrats was the skills that separated them from the commoners. The origins of the aristocratic distinction is that they had the time and resources to train at war, while the commoners had to throw everything into producing the necessary goods for survival. Even if nobles had lesser-birth companions as children, the practice of arms is one area where the line would be drawn. Granted, WoT is at the stage where those distinctions are becoming moot, and there is a rising middle class on the verge of breaking out, but that means there are also far more profitable and productive things to be putting boys to work at, and the martial practices are even less well-regarded. At an earlier stage of societal development, parents would have embraced any opportunity for a boy to train at arms, because it was a way into the elite. Now, when they can get rich, it isn't worth the trouble.
Which speaks to some general training as militia in many districts throughout the main continent. For the most part the majority of the nations have small formal military but have reservist style troops who likely spend the majority of their time as farmers or in a trade of some sort. I would say that these are the men most likely being referred to here as they would have received various levels of informal training.
As to the Seanchan ... mostly agree, but I do think it says somethign that only women have held the throne for centuries. Seems more akin to the Queens of Andor coming to prominence originally from a lack of male heirs, but also aligns well with the general gender role reversal RJ was building for the majority of societies. In his reality men committed the "original sin" and thus had a generally lower place in most societies. Even when it was relatively low key.