I'm working on an app and I want to display a male symbol or female symbol for a list of GKPlayers whose photo's can't be returned from GameCenter. Is there a way to determine the gender of a GKPlayer?
Not directly, No. (Even with private API.)
However: If you can use private API, then it looks like Facebook user ids MIGHT be available for players that have opted in:
https://github.com/nst/iOS-Runtime-Headers/blob/master/Frameworks/GameKit.framework/GKPlayerInternal.h (and GKPlayer.h, same place)
You might then be able to fetch gender info from Facebook.
The usual warnings about private API apply, of course: fragile, Apple won't allow it in the store, etc etc. Also, be aware that correlating a GK Player with external identity info violates the Game Center Terms of Service.