Why Does Playboy Appeal to You

First, Christy Mahon in Synge's The Playboy of the Western World hasn't always appealed to audiences. The play caused riots when it was originally produced because it was thought to be too vulgar, violent, and negative toward the Irish people.
Since other audiences/readers are further removed from the play's subjects, they may be attracted to Christy. Several reasons for this exist.
First, other characters in the play like him. This can be contagious.
Second, he bucks tradition. He doesn't follow stuffy protocols and traditions.
Third, he is a bit offbeat. He's an antihero. He moves from timidity to fame. He's a bit of an underdog.
At the same time, your premise may be faulty. The power of the play is probably achieved by the reader's not being drawn to Christy. That's the point. He is no hero. He gains fame by killing his dad, and then is made into a hero for his athletic prowess--he dominates in a little village. Not exactly Super Bowl stuff.
The power of the play is in the fact that the audience is bewildered by Christy's success. The other characters make him into a hero, when he actually does nothing heroic. The play, in part, is about myth making. Myth making is exposed, and the Irish villagers are exposed to be obsessed with violence, not too bright, and fickle.
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I had a favorite class in college that included work by J.M. Synge and his relatively straightforward presentation of his characters was probably one of my favorite things about his style. The fact that the characters really seem to respond the way people I know might with all their oddities and sometimes crudities intact is in a way refreshing if you are used to more idealized characters. At the time, and as others in the post below mentioned, audiences were at certain times offended by the very realistic and somewhat explicit way that the characters responded to things. So it isn't always for everyone, but I tend to think it is a valuable part of Synge's