It's not tied to a Google account, it has a better end-user experience, a better developer experience, and an extremely credible team behind it. That said, if you were using Google Auth and I assessed your application, I wouldn't ding you for using it.

Google Authenticator isn't tied to a Google account, and developing for it involves implementing a single algorithm.

Well the Google Authenticator application is just an implementation. I can use any TOTP generator to get access to my Google Account, or alternatively if I use the PAM module they've provided, I can use whatever I want to generate my codes to log in to my Linux machine. It just so happens that they use this mechanism for their two factor auth for Google Accounts.

I definitely hear you on the better user/dev experience. That's very clear from the variety of methods and slick screenshots they've got.