That reason is because it's not just this forum but how the Japanese, people who have come up with it in the first place, also use it. There's quite a few Japanese games with NTR right in the title which use this broader concept of "the girl i like/my sister/my mother/whoever that i don't have actual romantic relationship with is fucking dudes who are not me".
And yes, this can be considered silly and overreaching. But NTR is primarily about experiencing emotional anguish caused by someone you have feelings for having sex with someone else. And feelings don't care much about the logic or if you have a receipt of "established relationship" to somehow validate them.
The problem is that even NTR fetish stories that have the scenarios you are describing still have their stories
designed to evoke feelings of loss and anguish.
They follow the structure of:
1. establishing the strong emotional connection/dependence between the MC and the girl
2. build up how the "cheating" comes to happen (usually presented as a consequence of "weakness" from the MC: squandering an opportunity, a form of inferiority, or failing to "scare off" someone that might "take" something from them)
3. then finally we get to the consequence of the "cheating" and how it results on the MC "losing" their special person (it can range from a direct separation, or the MC feeling like they lost some of the respect/admiration/affection/attention their special person had for them, or even sometimes just the girl changing some aspects of her personality is taken as "losing" the special person by the MC who wishes they would stay as they were).
Now, I can understand referring to any case of displayed "infidelity" as being "NTR", even though I would say it could be technically incorrect if the writing isn't really conveying the previously described fetish. I do think just tags like "cheating" and "swinging" can be much more appropriate for those scenarios, but there is enough overlap between porn stories that feature cheating and proper NTR themes that I don't really find it very productive to be pedantic about it.
I can also accept the "alternative" forms of NTR that don't involve established romantic relationships as being true depictions of the NTR fetish, AS LONG AS the writing is noticeably designed to convey the feelings of loss and anguish that are essential to the fetish. I would even say those alternative forms need extra care, because the "girl I have a crush on" version can quickly slip into some dumb incel stuff, and the "my mother/my sister" versions can feel like just externalizing childhood trauma (struggling to accept a new step-parent for the first one, and abandonment issues over an older sibling changing their personality and moving to a different social circle due to the age gap for the latter).
The really stupid stuff that I personally can't accept is when people take the fact that you
can have NTR stories without established romantic relationships, but ignore all the missing fundamental requirements that make the NTR fetish what it is, and then start calling
everything NTR if the MC isn't at the center of every existing fuckpile in the universe.
And before someone even goes there, there is "death of the author" and there is "delusion-fueled media illiteracy". Other people can't control how you feel when you read something, but you can absolutely be branded as insane or moronic if you blame the author for things that aren't even in the same ballpark as what they were trying to write, it is like reading your cellphone's manual and complaining that it makes for bad poetry.
