I commented on a help topic about this a couple years ago. I expect applications to be able to cleanup on shutdown. Spotify is the only one I've seen in probably a decade that doesn't, and I don't feel as though I should need to explicitly close it every time I shut down my PC.
The desktop client doesn't handle shutdown at all, it simply closes without doing any cleanup such as saving state (like current song/playlist, settings, etc). It's well documented that there are events that can be handled for shutdown, which Daisy from the help topic linked above implied were useless.
I'd expect this to at least be in the Windows Store version of the app.
As a note and in response to Daisy in the help topic linked above, the "varying circumstances" in which Windows can shutdown without closing programs, as far as I know, are bluescreens and clicking "Shut down anyway" when Windows tells you there are programs trying to close. In neither case would I expect any program to close cleanly.