Lots of people reporting the same problem in the community here:
The issue is that rather than a player interface appearing a page is shown telling you to enable playback in the browser. This is a recent change.
Note that for many users in work environments changing the browser and installing software are not an option. Also I cannot use mobiles or tablets in the workplace so IE 11 is my only portal to Spotify at work.
Can someone at Spotify please comment on this?.
We've created this post regarding this topic, in order to clarify the situation. As we released a new web player a few weeks back, only the following web browsers meet the requirements to run it: Chrome 45+, Firefox 47+ and Edge 14+. You can also check this info here.
We understand how you all feel, and that many of you don't have access to a different web browser. Have for sure that we'll pass all your feedback on to the right team.
Any other questions that you have, don't hesitate to get back to us.