Come to think of it, MNG doesn't really fit NTS - it's more about the MC giving permission for the partner to experiment, not actively orchestrating the encounters.
Netorase (寝取らせ) isn't just "letting" your partner mess around — it's when the MC actively sets up and organizes the situation so their partner ends up with someone else. The causative form in Japanese here means making it happen, not just approving it. If it was simply "allowing," you'd use something like yurusu(permitted) NTR instead or just swinging. Well it is common for western games to have this type of swinging where the initiative comes from the partner, not the MC