I'm having the exact same problem on Ubuntu 16.04. Spotify 1.0.70 (installed from a snap package @ Ubuntu Snap Store) is not properly integrated with the sound menu in system tray. Spotify 1.0.69 (installed from a DEB package @ spotify repo) had the integration working. Didn't try 1.0.70 packaged in DEB though to blame solely Snappy packaging.
Any support on the issue would be much appreciated.
Yes, I meant the latter menu you posted. In my case, the Spotify section disappeared, having just the Rhythmbox one. In my sound settings, in the Applications tab, the Spotify icon is not recognized though as well.
I see this problem now as well. Either something has changed in the rest of my system, or more likely it has never worked well and we have just tested this on systems where you previously had the debian package installed.
A fresh snap-based install (purging all Spotify configuration files) has the same problem. So seems like previous deb-based installation doesn't affect a snap-based one in any way. It's either a bug in 1.0.70, or in the snap-based packaging itself (can't exclude the latter since the latest deb-based package is 1.0.69).
I'm also unable to connect to my chromecast on the network, but on the same computer I can access it with the web player. Please fix this, it's completely broken! One of the main reasons I subscribed to Premium was because Linux was supported. Uninstalling for now until it's fixed.