Google seems to pick and choose when they'll make a native app and when they'll go the web route with iOS. For Google Music, which is still in beta, they chose the web app route and it's actually still pretty good.
It's all powered within the Safari browser, you can swipe left, swipe right to jump between categories like Artists, Albums, Songs, etc. The songs stream from the cloud and even play in the background even when you close Safari. [Google Music via TechCrunch]