Only a couple of the possible push notifications are currently enabled, like a game start.

We're being very cautious with push notification. It would be quite easy to end up with several dozen pushes being sent to your device for say combat losses. That's something we want to avoid, and we also need to stay on Apple's good side and not have them revoke our access to APNS because we went crazy with notifications.

So push does work, but it will be a while before you will see them for all the possible events. I'm not going to enable a push category until I'm sure it won't send you 50 pushes an hour.