Yes it is. NTR isn't the same as cuckoldry...just bad mtl and people grouping them together. NTR is someone you really care about/love being fucked by someone/people when YOU don't want them to be. Has nothing to do with them being a slutlord. Basically cuckoldry but no romantic relationship between them I suppose?
Just want to clarify some things. Your example of someone you care about fucking other people can actually be written to be not NTR. MC has loved his childhood friend for a long time, but is too scared to confess his love. She starts dating some other guy. It is a healthy relationship. They love each other and he treats her well. MC is jealous and hates the guy for "stealing" her from him. He eventually accepts that she is happy and even comes to befriend the guy. She marries the guy. She still cares about the MC deeply as a good friend. MC eventually meets another girl. The end. Lol. That isn't really NTR right? This can actually even be a very uplighting or bittersweet story. Something you might see in some korean drama or something.
The most important thing that defines NTR is the bond between two people being broken due to some third party. The girl needs to fall into lust and corruption by the end. She must reject the bond she once shared with the MC.
Lets take the above story and change it a little bit. Same beginning but the other guy is a real playboy. He is known to corrupt girls and throw them out. The childhood friend rejects this guy's advances at first, but he is persistent. Eventually, he fucks her through whatever means (drugs/blackmail/seduction/etc). MC is very jealous and worried. The childhood friend gets corrupted by the guy. She is an aphrodisiac junkie and got tattoos and starts to treat the MC like an insignificant trash. She doesn't care about their friendship anymore. MC goes into depression and becomes a shut in. Every month, he gets a DVD of her getting fucked by all the hooligans and she talks shit about the MC in the video. He jerks off to the videos. The end. That is NTR.
So yes, there is normally a bond between mother and son. If the mother falls into lust and corruption and starts to neglect the son, that is certainly NTR. A mom having sex with dad/boyfriend/some random dudes is NOT NTR in and of itself, unless the story is specifically designed for it to be so. In games like this one, its pretty much inconceivable for the mother not to slowly/rapidly fall.
This is why I always say that NTR as a fetish needs to have a dedicated story that aims for it. Most of the optional NTR games and the "NTR" that people scream about when a potential love interest is fucking someone else, doesn't fit the bill. They will still cry about it, and I agree that NTR is the closest thing we have as a tag for such things.