You may not be aware of this. Also if you have Windows 8, try outcoldplayer
edit - Found an article where Google have stated that they are working on a full music player which sounds promising
There is a pretty nice desktop client available here for Windows:
http://apps.codigobit.info/2011/10/google-music-desktop-player.html
It is basically a wrapper around the site with some improvements, but it works well. I know you said you didn't plan on actually making an app, so I thought I'd point out there is at least an option on Windows. There is also some insanely priced one in the Windows Store called Gmusic, but the two aren't related. The desktop one is free. I love Google Music, so it's nice to have a stand alone client for it.
Using Chrome u can make a Play Music shortcut which kinda acts as separate app(no browser stuff like navigation bar or adress bar etc), also there is unoffical app which works great.
I found this one which has worked very well so far. It's basically the website in an application that supports media keys, has last.FM scrobbling and some different styles (which you can even make yourself)
It's great for me because I want to have as few tabs as possible open, and it also makes me able to mute chrome while still listening to the music. :-)
Google Play Music: http://apps.codigobit.info/2011/10/google-music-desktop-player.html from: http://vhanla.deviantart.com/art/Google-Music-Desktop-Player-413683928
Google books can only be accessed from browser I believe: https://chrome.google.com/webstore/detail/google-play-books/mmimngoggfoobjdlefbcabngfnmieonb?utm_source=chrome-app-launcher
I just started using this third party program for Windows and so far it hasn't buffered once! It's not perfect, I'd much prefer the normal site to work since I use some great Chrome extensions for it like Music Bubbles, but at least this works!
Sorry for the late reply, that is the Gmusic player, it's a bit buggy but it's the best free one avalible atm
I think you're talking about the Windows 8 (store) app right? I tried the new version but the fact that it is a windows 8 app limits its functionality in two ways:
This is the program I was talking about. It isn't actually called GMusic, my bad.