Mercutio is neither a Montague nor a Capulet. He comes to feel that he must defend Romeo's honor when Romeo refuses to cross swords with Tybalt (who is a relative of Juliet). Romeo does not want to be held responsible for any death that would put him in bad light with Juliet.
So Tybalt and Mercutio duel. Mercutio lies dying as he utters his famous curse. A plague is a horrible thing to die of. Mercutio is saying that both houses need a swift ending -- in other words a plague to visit them.
Of course it does. Both parents suffer great loses by the time the play ends.
