NTR refers to a fetish where the viewer/reader has a vile/hateful/disturbing fascination over one partner of a couple who has a sexual affair either by forced or choice. It means we hate it when we read/watch that person in that situation(especially if it was against their will) yet at the same time fascinated by it.
Whats happening between Rygart, Hodr and Sigyn is not NTR(heck there's no sex!) but a sympathetic affair, an affair we know is wrong yet at the sametime we can't help but feel sympathy for the people involve in the affair and the reason they done it.
An example would be a young woman who has an affair with a kind man behind her cruel, uncaring, older husband. In this situation we know what she's doing is wrong but we sympathize her since her husband is a cold, uncaring man who never really love her and saw her as a trophy wife whiled her lover is kind, caring and understanding man who truly loves her. Another example is Hank Rearden and Dagny Taggart from Atlas Shrugged. Hank is a rich, genius inventor but his family, especially his wife, don't care about him or appreciate how much work he's done to support his family as they only care about the money he brings. As a result, Hank has an affair with his boss Dagny since she's sympathetic and appreciate his genius and the work that he's done. If you want one more, watch the movie
Waitress starring Keri Russell and Nathan Fillion.
Now back to Rygart, Hodr and Sigyn. Since i read the manga, there are some things i know more about their relationship than you know from the movies. Despite what you believe,
Hodr doesn't love Sigyn, he only cares about her and her safety as a friend. He's also aware that Rygart has feelings for her and even encourages it! Hodr and Sigyn don't love each other but Hodr knows she loves Rygart but he gave it up so she could have a better life. In order to bring those two together, Hodr encourages an affair between them!
I would love to say more about their current status in the manga but it would spoilerrish, so let's talk about that in the manga thread.