That's just an average harem game, even including the women being excited seeing their man having sex with other women and aiding him at getting other women. It's just not typically further elaborated or focused on from that specific perspective.
Way I see it, the difference between harem and NTS/NTR is origin. NT comes from a single person relationship, in wide sense. A girlfriend, a wife, even just a crush or even a mother or daughter (specially in NTR - in a sense of "losing the love" for lust). Thing is: there's an emotive relationship between two people, and it's expected that remains between two people.
Harens comes from a diferent premise. Here comes from an open, or semi-open relationship. It's when one person vinculates to several others of the oposite sex or not! There's not individual, but a multidirecional relationship. There may even occur conections between the members, not involving the cental figure (despite being rare). It's not expected relations only with the harem's core.
The key here is that every person involved knew about the open nature of the bond since before it started. On the NTS/NTR, the bond begins closed, until a third party enters in it, either invited (NTS) or unninvited (NTR).
In harem stories, there's no jealousy, envy, or sense of possession, unless it's a political harem (Sultan harem, or Emperor harem - see Kusuriya no Hitorigoto for example). In NT stories, as there is possession, in the sense of one's feelings belonging to the other, and in reverse, with the entry of the third party, there is a feeling of invasion of personal space, fear of losing this space and jelousy for seeing another ocupying this space. Those are exactly the feelings that trigger the excitation, the arousal, that characterize the fetish, and the anxiety, angst, and even depression depending on the development. The duality between arousal (which attracts) and anxiety (which averts) cause doubts and, depending on how it unfolds, may further depression and cause insanity.
Which maybe is where this MC is getting close, at this point of story! He can't get aroused by normal means anymore. But the process causes him so much pain, angst and emotional damage, that each ejaculation makes him feel relieved, but not better! It's already in the point of "I don't even know how I feel, anymore". And the suport he gets from his wife is becoming each time more provocation instead of reassuring, what only intensifies the feelings (good AND bad ones).
So, in my opinion (due respect to contrary ones), harens and NTS/NTR are fundamentally diferent, not to be confused, because the dynamics between its components generates different expectations!