Yeah, but again, it is a matter of perspective, and the other two types are generally only called NTR in Japan, at least outside of these discussions. The others are usually called cheating or sharing respectively, when we are talking about tags.
As for this game, we are talking about how the PLAYER feels about it, not just the MC. If it makes the player/reader feel jealous, then it still NTR. You cannot define your way out of how someone 'feels' about something.
No matter how you try to define it, if the women in the game do any sex acts with anyone other than the MC, you are going to get people who define that as NTR, because it makes them feel jealous. Telling them that they are wrong because of some technicality, doesn't make anyone feel better. It makes them more offended, starts arguments, and drives those people away. And if we are talking about the definition, it includes the audience, not just the people in the story, people forget that part of it a lot of the time when discussing this. It can be either, or, or both. Some of these players don't even like the women in their harem kissing each other, which is as benign as it gets.
Having your girl go sleep with someone else, is the definition is cuckolding, especially, if you get off on it, which is why your game gets the NTR tag. Whether he has feelings or not, he had his girl, sleep with other men, which is there to either turn on, or make the audience jealous.
Oh well, not sure how I got sucked into this, but hope that helped some. Good luck! I hope this, and your new game do well.
Side note, you might want to add the new game to the OP here, and maybe update the non-working links, like Nopy. You can petition to either ask the OP to do it, or ask for control of the OP, so you can do it yourself. Take care!
