The player is a web version of the music service inside an app, you need to first login to your Google Account and then access the Google Music.
For me it seems like Google Music is a complete waste of time. You can simply sign up to Spotify and use their amazing player for your locally hosted music. I know that your music with Google Music is hosted in the cloud, which is great, but its just a very basic service and its only as good as the devices I can get the service on.
Anyways, if you want use Google music then check out the Google Music player (not official version).