The issue is that on the desktop client, you cannot save music from "Your Library" offline at all, you must create a playlist.
Notice that there's no way to make that particular album in "Your Music" available offline.
Yet on my Android client, I see a Download option near this album to make it available Offline:
The only items that present such an option on the desktop client are playlists as shown below:
On iTunes (Apple Music) however, I can make anything available offline on my desktop:
This for me is the biggest problem with Spotify and why I'm currently an Apple Music subscriber. In general, the desktop client lags behind features on the mobile clients which are actually far better.
There are many more examples of differences that I can demonstrate, but this is the most important.
The ability to make My Music available offline on mobiles appeared more than a year ago. Can we please have this and further differences addressed on the desktop client soon?
Thanks for coming to the Spotify Idea Exchange and voting to make this happen.
We're happy to announce that this feature is now available on Desktop. You can now download not only playlists, but also albums and podcast episodes by clicking on the download icon so that it turns green
Once again, thanks for helping us make Spotify better, by participating here on the Community.