LOL @ Johnny! Yes, it may be time to split.

Her guy and I aren't going to become drinking buddies, but the fact that he's made these little overtures spells trouble. Maybe he's just a really nice guy, but if that is the case and that's all that's up, then still, it's time for me to move on, because it's not like I have some long-standing relationship with the woman either.
Playa....LOL...more like dirtbag...sorry Tre...I'm not down with O.P.P.
Your whole issue lies in that second 'P', because you're indicating by your tone that you feel that the arbitrarily assigned titles of 'boyfriend'/'girlfriend' carry with them certain rights, privileges, and obligations that rise to the level of a married or even engaged-to-be-married couple.
There are too many people who are under the spell of 'coupledom'. You've been conditioned to believe that the 'couple' is some vital unit which gets to police not only the behaviors of its members, but also the behaviors of others outside the 'couple' as well. Needless to say, I'm not at all a fan of the social policing power this arbitrarily-created unit has been granted over the generations.