As someone who hates the genre with a passion, NTR has a very strict definition, namely having your partner *in a romantic relationship* be stolen away from you by another person either through emotional, mental or physical means, resulting in said partner's feelings switching from you to that other person.
Seeing your widow/divorcee mother remarry to give you a new stepdad? That's not NTR. Same with seeing your sister get married to the guy she loves, that's not NTR either.
You're a high schooler who has a crush on a teacher, and yet she only ever sees you as a student while she goes for a relationship with a college student? That's not NTR, since the partner in question never had romantic feelings for you in the first place, no matter how strongly you felt for said partner. Otherwise ALL harem romcoms in history would have the "NTR" tag labelled on them.
The two people are in a romantic relationship, but their feelings have begun to cool off and have even become hostile, and now the guy finds himself a girl who he now loves more? That's actually not considered NTR, due to the people involved having an emotional falling out and thus the romantic relationship can no longer be said to be mutual.
NTR is if for example two people are in a stable and happy romantic relationship, then suddenly a casanova comes along and successfully seduces the girl thus making the girl love said casanova more at the expense of her former partner. THAT is NTR.
A main component of NTR is that both parties in question must've had a mutual romantic relationship with each other, which is what makes one of the parties suddenly having their heart swayed and falling for another person be very effective in portraying the feeling of a person's feelings being "stolen". You can't dilute NTR to include stuff like "childhood friends u were in love with but never made a move", because that's not what NTR is about, otherwise you're labeling everything involving relationships whether familial, platonic or otherwise as NTR due to the complexity of relationships between people, which makes the definition pointless due to an absurdity.
Note that emotion is a major component of what makes NTR what it is, and while NTR is often used as a vessel for stories centering around sex, it doesn't necessarily have to involve sex to be NTR since it's the emotions between parties that are important, and thus can actually exist outside of hentai.