playAppleMusic.com

It didn't work for me. The first time, I logged in successfully and gave the app permission to access my Apple Music. It loaded my library except for Playlists, but was unable to play any song. Then I tried it in another web browser and it stuck after Apple ID login. I tried several times but have the same problem. It might have some technical issue or something but stucking after login doesn't seem okay from a security point of view.

The UI is a bit on the ugly side, but don't let that detter you. The web player works pretty well, has a bug here and there, but it's pretty much the Apple Music experience. Plus, if you open the site on Chrome you can cast the music to any compatible device (something Apple won't let you through iTunes or iOS).