Like the Chromecast itself, the app is (strictly speaking) US-only for now.
The Chromecast app is universal, free, and supports setting up and managing a Chromecast device; casting itself from an iOS device still comes via the YouTube and Netflix apps only at this point in time.
It’s a welcome inclusion to the Chromecast’s abilities, although there’s a tiny bit of me that’s surprised that Apple approved it; it’s not as though there’s much love lost between Apple and Google these days.