It was discussed already, there will be NTR depending on choices it seems. Most likely, I assume, based on what is said, you'll make choices where his girlfriend will do activities with other men without telling the MC about it, unlike agreed to. So despite being in an open relationship, they will pretty much be cheating. And if your choices are the MC remains faithful during it (and maybe even rejecting all other girls, so not even being open), NTR will be happening.
If it's what I think it is, it's simply just the NTR is your choice. It also sounds like the reverse can happen too. You can make choices so the girlfriend remains faithful, and the MC is doing stuff with others without her consent at all. Arguably a reverse kind of NTR, personally the one I'm more interested in seeing.
If you both are doing stuff with others, and telling each other, you're basically going down the NTS route (netorase). And, there's at least one other character you can potentially steal another girl from a different character (netori). Basically, it has all your different kinds of NTR kinks in it, and more, but it will be based on your choices, not forced on you if I'm not misunderstanding. Therefore, if all you want is the MC to get cucked, it sounds like you'll get your wish, just make the right choices for it.
Oh, forgot to add, but as of this current version, (v0.1), there's no NTR "yet". Just it sounds like it's the creator's plans for the future.