This occurs with both the Windows 10 Store version and the Win32 app.
With Spotify running, if I shut down my PC through the start menu (or simply kill Spotify through Task Manager), Spotify will revert to any settings that were set as well as whatever playlist/song was playing when I last cleanly exited using the Exit button in either the tray or File menu.
The more I use Spotify, the more frustrated I get having to manually close Spotify every time I shut down my PC. After nearly 3 years, it's still not something I've gotten used to, nor should I. Every other program has the capability to do this.
In response to Daisy here, applications can detect Windows shutdown (example), and can even prevent shutdown until the program cleans up and is ready to close.