Well you're mostly right... although a hotwife is just someone who has sex with others outside of her marriage, it has nothing to do with being the wife of a cuckold. It's just a wife of someone who gives his consent and even encourages her to have extra-marital sex. Yes, in a lot of cases the guy IS a cuckold, but it's not necessarily always the case. Cuckolds by nature are submissive and view themselves as lesser to their partner's other lover(s). However, in the case of the MC and Mary, their dynamic has always been much more like a stag and vixen, especially since the MC is also allowed to have extra-marital sex with the wife's permission.
To get really technical, in hotwife relationships, the guy isn't supposed to be have extra-marital affairs at all, so even the hotwife path in this game is more akin to a swinger relationship. However with the wife having much more freedom, it's basically an open relationship on one side, and on the other side the husband being allowed to swing with the wife's permission.