The point of view and the focus on how the story is portrayed, makes it NTR. Cheating is not needed to be NTR neither cheating has to be NTR.
If there's a story of a married woman banging a random dude, that is cheating, not NTR. Still bad ofcourse, but a different kind of bad.
If there's a story of a woman banging a random dude, where the story is being seen primarily by another love interest whose has a crush on her, his thoughts, his feelings all of this while showing scenes of the woman banging another dude, it's NTR. Does she owe him sex or anything like that? No, she owes him nothing but the story is being told this way to showcase the pain of a character. However usual NTRs tend to go the extra mile and add cheating to it so the pain is multiplied.
Genders can be reversed, but it's more popular to see the male in pain.
I'd say that NTR is about the mood of misery, betrayal (forced due to e.g. blackmail or willing) and suffering. Like Visual Novel game about romance, but where you clearly got the Bad End, or when someone wrote edgy Bad End fanfic to the story. Like T-sama wrote, you can write NTR-style story about kid, whose bully shows him the video of kid's mom getting banged and abused. On the other hand, classical porn movies with milkman or plumber banging hot housewife, where we never even see the husband, aren't really NTR despite technically involving cheating, and nobody every had a problem with those.
The focus of the story is important, that much is true. Imagine a story about woman forced to marry a guy she hates, for example threatened by yakuza who's lusting after her, and when she's at the altar , priest says "you're now husband and wife, you may kiss the bride" and at this moment her childhood friend - who once promised to marry her - swoops down from the chandeliers, runs away with her on a bike and jumps into speedboat, leaving the bad guy to watch through binoculars as the reunited lovers immediately start fucking on the boat, far away from his goons, she still in her bridal wear. The bad guy would totally think he's being horribly NTR'd here, he's forced to look as his wife is letting herself be fucked by another guy who took her from him, but the readers will consider it wholesome story of pure love triumphing over NTR. I think that difference between character feeling NTR'd and story feeling like NTR to readers is also important distinction. If we're clearly meant to sympathize with the character's feelings, then IMHO it should count as NTR or at least NTR-like.
Though it's also true that, like slyss wrote, some people are being delicate snowflakes who see NTR in relationship of any women in the story (not the love interest) with some male other than MC, and that's just dumb.