Why does the playboy appeal to readers of The Playboy of the Western World?

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.