INTERNET and ACCESS_NETWORK_STATE are necessary to send data over the wireless network, and without that ability, the app would be pretty useless.
ACCESS_WIFI_STATE is to be able to detect the Wifi state, so that the app can display a warning if Wifi is disabled.
WRITE_EXTERNAL_STORAGE is for caching album art, to save network traffic.
BILLING is to allow users to buy the bonus features through Google Play.
INSTALL_SHORTCUT is used when you create Library shortcuts on your homescreen.
READ_PHONE_STATE is used when performing actions if you’re getting a phone call (like lowering the volume, or pausing the music).