Gifting an app I've already purchased for myself

I want to "gift" an app to a friend and am apparently unable to do so. The directions say I can click "buy" next to the app in the iTunes store, but this is grayed out for me since I have already purchased this app for my own iPhone. How can I gift this app now to someone else? This is a GameCenter game, that we can play together, if I can gift it to her.

Thanks!