That's... not how it works. There's "reverse NTR", which is when a boy is stolen from a girl. Then there's avoidable NTR (where you can prevent NTR with right choices). Anti-NTR is a term that would rather fit a netori genre, where you're the one stealing the girl. Netorare - your girl is stolen, netori - you steal the girl. As for what an anti-villain is, it is usually just a good guy acting like an antagonist, or someone with noble intentions doing ultimately evil stuff, or more traditionally a villain who lacks traditional evil qualities. In general, this term is less concrete and well established than anti-hero, which is a hero who lacks superficial heroic qualities (think Witcher). But the use of the word "anti" in those terms isn't "how English works", rather it's an EXCEPTION. In general, "anti" means the opposite and something that fights the thing. Anti-magic isn't a form of magic, it's something that fights magic, anti-personnel weapon is a weapon against persons, antifreeze is something to prevent freezing, etc. What's the point of trying to invent a term when your game doesn't have anything that wouldn't fit the general tropes?
In a way, anti-NTR is something you can call a story like " Makeine: Too Many Losing Heroines! " where the guy gets girls after they are rejected by their crush, as it doesn't fit any of the established genres. By the description it seems your game is just a typical avoidable netorare game.
