Hi @DorianJ, welcome to the community!
That's odd!Have you tried going to both play.spotify.com and open.spotify.com? Both are Spotify web players.
I have the same problem. If I go to play.spotify.com on my surface rt i get redirected to open.spotify.com and on that page i get a page where i can only play 30 seconds clips and i do not get the option to login.
To make the Spotify Web Player working on Windows RT, please follow this guide: https://forum.xda-developers.com/showpost.php?p=75441695&postcount=557.