In your spotify desktop version, you can click on your profile right on the top. Click on profile/account and after this on setting gatget/device key. Now you can see your personal username, which are numbers. below this a button to send an email for setting the key. Now you have the possibility to set a key. After this you can login with the long number and the key.
The main (if not only) reason for purchasing the Gear was to listen to Spotify in the gym.
I cannot use wifi in the gym because my gym requires me to enter a username and password in a browser (another thing that is not possible on the Gear S3!) to connect to wifi as it is public wifi.
So, I want to at least take advantage of the offline function of Spotify and the Gear. This is not possible as it keeps hanging when pressing the Play button. Deleting the cache and redownloading it all again works but to do this every day? That was certainly not advertised as such!
Finally got Spotify offline feature to work on the Samsung Gear S3 (without having to delete and re-download music). I think the same applies to Gear Sport:
What I had to do is really go offline - manually. That meant going to Spotify settings and select Offline = On. This tells spotify that my watch is offline and that it should stream music from the cache. Why this does not work automatic (i.e. when I am not connected to wifi or my phone's bluetooth) is beyond me.
Anyways, I'm glad I found a solution and can now use my Gear S3 in the gym as planned in offline mode! :)