But he doesn't know about Max's feelings until after he is already in a sexual relationship with his mother...He who shall not be named knows of Max's feelings and trys to remove him from the game (you get a game over if you fail) so he can have his way with the entire family. NTR in a nutshell right there.
There is no relationship other than Mother Son...
By your definition, His father if he was in this game would also make this an NTR game if he slept with his mother...
I prefer the Urban Dictionary definition...
You must be registered to see the links
Max is never her partner in that description so the only one being Cucked is Eric and only after Eric is gone with the exception of a HJ you can get when massaging her while he is still around.literally means "You must be registered to see the links" and shortened as NTR is a hentai genre where in a heroine will be introduced as having a significant other, which may be a husband, a boyfriend, or even a partner in a BST affair. The story will then show the aforementioned heroine being intimate with another man thus provoking jealousy in the audience by proxy.
If Eric had appeared AFTER Max had the sexual relationship with his family only then it would fit the situation you are looking for.