People tend to think of relationships as binary. You are either in a committed relationship or you are single. A non-binary relationship is where you are fucking someone, but also free to fuck other people - like friends with benefits or the dreaded "it's complicated" relationship status.
Him: so who is this guy you are seeing.
Me: Well I don't know if I would call it all that -we are free to be with other people too - its a non-binary relationship.
Boys who enjoy yaoi (a genre in Japan that contains sexual and/or romantic relations between two men); literally translates to "rotten boy"; corresponding female : fujoshi