One type of NTR I've seen, that doesn't really have a specific genre tag that I've seen that doesn't contain cheating or rape or blackmail, is for instance a guy has a crush on a girl, he's planning to confess to her, and out of left field comes another guy who "steals" her away. Two good examples are some hentai mangas Chitose and Leftovers - Classmates Who Lost Their Virginity. Some guy moves faster than the MC and so the girl gets "stolen". It gives kinda that feeling of NTR without the cheating.