Spotify can be listened in 2 ways. one way requires a spotify premium subscription, the other one, requires for the speaker manufacturer to have a business deal with spotify that certifies the speaker as spotify-able which in turn given them restricted acces to the spotify API that can be called from third party apps, like the sugrcube app.
For the spotify connect case, you need A) Phone or B) a pc/mac/linux machine that has a running spotify app open, in the same wifi network as the speaker. it then re-streams spotify music to the speaker via spotify connect.
For the other case, as I said, the controller app has limited accessibility to the spotify api, and can make remote calls. BUT you still need the spotify app to manage playlists etc. You can only skip tracks, set repeat/shuffle,etc. The thing spotiy want people to use their app instead of third party ones. For this case you don't need to have the spotify app open unless you want to edit playlists etc.