There really isn't a playboy per se in Midsummer's. There are, however, three characters who we can see as commenting on the games of love from a male perspective. First, Oberon. He and Titania play power games that disrupt, quite literally, the entire natural world. He would communicate the idea that the playboy brings destruction. Second, Puck plays games with the young lovers, Demetrius and Lysander. Both of them show how arbitrary love can be; they seek whoever they currently love, and don't realize how foolish they look—or, more importantly, how much they are hurting the woman they supposedly love. Third, and most simply, there is Bottom. He has the head of an ass, and he acts like one, because he accepts Titania's praise as his worth. He is every man ever taken in by female flattery.
Together, they point to the universal nature of the playboy figure, which is forever damaging and limiting.
There is some relevance of the Playboy in the book compared to the modern society as there is still a taste of love from the male perspective of the whole situation. The male characters are risking love in turn for success, and poke fun at the difficulties, tragedies and sufferings that the female counterparts who are in love had to endured, seemingly thinking that love is just a game for the opposite sexes, hurting their wifes who they were supposed to be taken care and loved for, not knowing how foolish to they were in clinging for false hopes and desires, making them into a complete clown