Yes, if it's a manga or a Japanese game, feel free to use Japanese terms. But if it's NOT manga or Japanese, why do that? We have a lot of western terms to use.
Extremely impractical. First, it is a tag for which you can search and which can be sorted. Then you would have to define which games precisely are "Manga": 2D graphics? Playing in Japan? Japanese author? 2 out of 3? Then after that is decided I have to reword everything because I am describing the same thing in a different game.
In a game taking place in the west, that "LI under no obligation to be monogamous" would be a "fuck buddy" or she may be in an "open relationship" with the MC. And if the MC still feels "jealous" in spite of the "no obligation to monogamy", just call it like that: jealousy. Why call it NTR?
Since we are in the world of fiction, there is something like "designated love interests", so there's way more possibilities. And jealousy can go way further, does not have to have anything to do with NTR, can already be triggered by the LI going out to the movies with somebody else.
Still an "open relationship", agreed upon by both MC and LI in which case none of them is jealous. And "doesn't care" can be even extended to "enjoys it", in which case the MC would be a cuckold. We have a lot of terms available to describe everything..
Or it could be a relationship where love has run cold, one partner is cheating but the other doesn't feel anything anymore, or more possibilities.
The thing is: on this forum, NTR is a defined term. Cheating is another, different term. They may not always be used correctly but in theory with this I can talk about certain kinks I like or dislike and everybody gets what I mean. Why it was used, I don't know - I am neither familiar with the Japanese variation of comic/animations, nor a fan of the kink. But when I talk to people here, they understand me, I understand them. And that is what is important on a forum. Getting thousands to change their vocabulary due to one person's preferences will be a Herculean effort. And just like "tsundere" as a character type description one needs to accept that there will always be terms coming from a certain form of art and transcending its origin to a more general term.