I don't understand why it doesn't have the ntr tag
Maybe because you actually don't know what NTR is? Let me help you:
To make NTR really mean NTR, as it is defined by the manga, where the term actually comes from, there are the following requirements:
There needs to be a relationship (a simple stabile relationsship, being engaged or married)
At least one of them needs to cheat on his/her partner
The cheater needs to be "taken away" from his/her partner.
The last requirement makes the difference between just cheating and NTR. "Taken away" means the relationship to break up and the cheater has to be permanently with his lover. It also doesn't matter whether the cheating is straight, gay or lesbian. Also not whether the protagonist does it or someone else in the game. It can also be a couple that has nothing to do with the MC at all.
So if someone, no matter if man or woman, cheats on his partner, but does not leave hin/her for the lover, i.e. is not „being taken away“, it is just cheating, not NTR. If a man/woman in a stabile relationship has sex with another person without the partner's consent, it's called cheating. But if his/her partner agrees, it is sharing, not cheating. And if there isn't even a steady partner, but someone has sex with different people, it´s nothing but sex. Got it now?
So now you can see why the game doesn't have an NTR tag. And you also know that an extremely large number of games are NTR tagged, even though they don't contain any. And still others are not tagged NTR even though they have it. NTR is almost always misunderstood and the word is almost always used incorrectly. Most of the time it is used in general just because a woman has sex with another man. But in most of all cases this is completely wrong.
You´re welcome.