Why does Pegeen refer to Christy as the only playboy of the western world?

First of all, let us define the meaning of the word "playboy" in this context. In contemporary terms, a playboy is a wealthy and privileged man who spends time enjoying life, and he is often sexually promiscuous. Certainly, this definition has relevance in the play; Christy slowly fosters a reputation for daring, and, as a result, becomes a sexualized figure that seems to be pursued romantically by many of the local women. However, that more modern definition of playboy is not completely adequate for us here. Rather, we might think that Pegeen calls Christy a playboy because he becomes an almost mythic figure, a narrative construct who, by perpetuating a fiction of patricide, is seen as a legendary hero by other Irish peasants. Thus, Christy is a playboy in that he can "play" the role of the mythic hero, the hero who accomplishes great tasks, such as toppling a patriarchal tyrant, and who can win any athletic game in which he participates (playboy here especially seems to suggest Christy's new dominance in all kinds of sports). The term is still ambiguous even with this definition, but I think that this ambiguity is part of the reason the play's popularity has endured.
Additionally, I think that we can safely say that "the western world" refers to the west of Ireland, where the play ostensibly takes place.