I think what he means

When Gunwoo says “we are already engaged” I think he is talking about the flower ring from years ago. I think Gunwoo thought it was an engagement ring. Later down the line (bonus points if it was in the same conversation) Lee A must have said something stupid. As a result, Gunwoo married his female friend who was chill with him being gay. Well time passes, and Gunwoo and his “wife”/friend divorce because she found love and he is still not over Lee An. So now that Gunwoo and Lee An are seeing each other he plans to propose to “right the wrongs” of their past. That is why his ex wife, who is probably his best friend, goes to help him pick out a ring and make plans to get engaged with Lee An. That’s just a theory… a gay theory.