The only other information that is useful is generic information. Specific information (name, address, credit card numbers, etc.) the app developers (me included) do not need -- they are only useful to Google Play/Checkout/Wallet handling the purchase transactions on the app developers behalf.
The language you are running the phone in could be used to prioritize/target translations of the application. The version of Android could be used to concentrate testing. Tablet vs. phone as well as screen sizes can give an indication of where to improve UI layout and presentation (although the devs should still ensure it is at least functional on those setups). The device the app is installed on can be useful for tracking down bugs and if a particular device is popular for the app, the dev can purchase one to focus testing.
The only other information is app specific -- e.g. what functionality of the app is being used / where people are spending most of their time. This allows the devs to either remove the functionality (no-one wants it) or figure out how to make it more discoverable (no-one knows it's there). This also applies to help -- which help pages are being read the most (indicating a usability/discoverability issue).