Zipf's Law is one of those wonderful rules of the universe which describe how things are, rather than why things are. Other examples might be Bode's Law (for the distance of planets) or Vizzini's Classic Blunder ("Never get involved in a land war in Asia").
It's major application (these days at least) is in explaining the popularity of competing services. Not the why, but just the fact that twice as many people use Google over Yahoo, or Facebook over Linked-In etc
It may even apply to the shifting sands of the Canberra chess scene. For reasons to do mainly with geography, Canberra has usually had 3 or 4 clubs in operation. Unfortunately, mainly to do with population, these clubs periodically go through periods of boom and bust. In an ideal competitive market, the busts would shake out the under performing clubs, leaving Canberra with one or two constantly successful clubs, rather than 2 successful clubs and 2 struggling clubs.
Anyway, the two clubs that are doing well in Canberra at the moment are the Tuggeranong Chess Club, and the ANU Chess Club. Indeed the ANU Chess Club is doing so well that until we get some bigger space, we are turning players away from our tournaments. Which is a little unfortunate, as obviously getting more players into the chess scene is obviously a good thing.
Now while the ANU Chess Club members obviously turn up to the club for a reason, I suspect it is more a "crowd attracts a crowd" mentality the motivates new players to change clubs. And while Zipf's Law doesn't explain this, it certainly does measure it.