It seems that the Safari browser is no longer supported for the Web Player. I've been using it for years without a problem. The Spotify System requirements page even says it can run in Safari 6 or higher: https://support.spotify.com/us/article/spotify-system-requirements/
I have Safari 10 on Mac OS 10.12.6, but when I try to open play.spotify.com now, I get the message, "This browser doesn't support Spotify Web Player. Switch browsers or download Spotify for your desktop" (see screen shot).
I checked the Switch browsers link, and sure enough, Spotify Web Player no longer supports Safari!
Thanks a lot, Spotify, but I don't want to switch browsers or use your desktop player!
Either restore Safari support, or I'm off to Apple Music, Amazon Music, Google Music, or something else. And while you're at it, dump Flash and use HTML5!
EDIT: I thought I replied to @SebastVAIO but don't see it, so here it is again:
play.spotify.com redirects to open.spotify.com and then I get the error message. Deleting cache and cookies has no effect. I contacted Spotify Support and this is what they said:
"After taking a look backstage, we can confirm that after recent updates Safari is no longer a supported browser for Web Player.
We're always testing things by adding or removing features to make Spotify better overall. We’re sorry that this means you’re not able to use the Web Player like you could before.
We can't say if or when any specific features will be back. But as soon as we’ve got anything to announce, we’ll let everyone know via the Spotify Community.
Sorry again for any inconvenience caused, and please let us know if there is anything else we can do for you.
Spotify Customer Support"
In other words, Safari users have no choice but to switch browsers or use the desktop app. I did a little experimenting (switched my user agent to Chrome), and I got a new message to "Enable player in your browser," which leads to this page:
Apparently it has something to do with the Google Widevine content decryption module, which Apple doesn't support because it's not very secure. I tried enabling the Widevine plugin and got the attached message. Looks like Apple is having a pissing contest with Google, Spotify, and anyone else who uses Widevine. In the meantime, we users are caught in the crossfire.