In other manga it seems to actually represent being someone’s lover. So I guess the “wrapped around his little finger” isn’t so off the mark but just not in a bad sense. He basically admitted he sees her as his love interest to get the other guy to back off.
I forgot to also mention in most manga when it’s something to do with a “red string of fate” plot they often have it tied to someone’s pinky finger so that could also be part of it or a representation of it.
So he admit that she's his "pinky"??? Like he admit she's his but still treating her like a toy. We got another clueless but possessive ml....