Can you open up your Desktop client press ctrl + P
Click "SHOW ADVANCED SETTINGS"
Navigate to Startup and Window Behaviour
Disable "Allow Spotify to be opened from web"
Have you tried, please, the following?
* Uninstall Spotify. (Later you can Reinstall Spotify 1.0.14 from >> this link. << )
Now in a FireFox browser, please try this link >> https://play.spotify.com/user/rednblu/playlist/5i44MpqdV8Oi3rjy9S4DAq << which should display my playlist of Ocean sounds.
In the lower left corner, please click on the Gears icon which should open the Web player "Settings".
In the screen that comes up, you will see a line "Play open spotify.com URLs in desktop app". If you hover your MousePointer over the CheckMark at the end of this line, you will see that the CheckMark is very barely green-- rather than gray. If you Click on that CheckMark slowly a few times, you will see that it alternates between Gray and VeryBarelyGreen.
* Click on that CheckMark at the end of the "Play open spotify.com URLs in desktop app" line so that the CheckMark turns the Grayest gray that you can get-- without any green. (laughing) Can you see it?
* Then Logout of all of your sessions with the "Sign out Everywhere" button under "View Account".
Now play any "HTML link" of a Spotify track, such as >> Turbo Fruits – The Way I Want You <<. Does that track now play in the WebPlayer as you wanted? (If the WebPlayer stalls in a "Spinning circle"-- just kill that FireFox TabSession and restart by clicking on the >> Turbo Fruits – The Way I Want You << link again. (smile and smile for every Spinning circle)
Screen shot follows-- of the WebPlayer "settings" that you want to use I think.