NO you have it all wrong Ann in not Max's girlfriend or wife she is his mother and other than that they don't have a relationship yet.
Did you even read what I posted? I didn't say that Ann was the wife/girlfriend of Max, I said that they share a relationship, a conection, in this case a familiar bond, since she is his mother, Ntr doesn't only involves girlfriend/wifes, that just cheating, NTR involves the feeling of jealously, it can be even from a future LI.
Acording to your definition, Eric fucking the sisters of Max or the aunt, won't be NTR, since Max isn't the boyfriend of any of that characters, yet you would say that's NTR.
There are multiple works, where it is labelled as NTR, even in games here, where the guy doing the NTR, is taking away the Mom/sister/friend of the MC, and in those works the MC isn't the boyfriend of any of the girls taken awya, yet it's NTR.
Many of this works are japanese, many comics, stories, vn are tagged or described as NTR by the japanese author and it doesn't involve a wife or a girlfriend, since if it was only about a girlfriend/wife fucking others guys, it would be labelled as cheating.
Here another definition of NTR from vndb:
Netorare (寝取られ) is a sexual fetish designed to cause sexual jealousy by way of having the heroine indulge in sexual activity with someone other than the protagonist.
For a game to be classified as Netorare the following conditions must be met:
1. The heroine either must be romantically involved with the protagonist, a potential romance for him or of someone that the protagonist shares such a close relationship (sister, mother, osananajimi etc.) that jealousy is a factor.
2. Related sexual events are explicitly shown to the player or later described in detail.
This does not include relationships of heroines that are outside the route you follow. Explanation: Route 1 is for Heroine A, the protagonist is romantically involved with her. During that route, if she sleeps with other characters than the protagonist, it would be NTR. But during Route 2, which is about Heroine B, where the protagonist has no romantic relationship with Heroine A, her having sex with others wouldn't count as NTR.