https://play.spotify.com allows you to run spotify in your browser, meaning you can run the application on the Surface RT even if the spotify app is not available (yet?)
If you do not have the required cookie on your machine to participate in this beta, you are redirected to spotify.com.
The key here is to get the cookie or open the following site: http://www.spotifyweb.tk/
This evening I noticed that IE became not supported, it is possible to change the user agent string so that you are able to run spotify in your browser on the Surface RT.
Select the gear icon in the upper-right corner, select F12 developer tools > tools > Change user agent string to Chrome…
Hope it helps!