I've seen similar issues dated about two years ago, but the only thing that seems to have worked was making a new account, which I don't plan on doing.
I used the web player on Google Chrome on my old Chromebook all the time. I just got a new Chromebook, and I believe this is the first time I tried to use the web player. Each song gets skipped within 2 seconds of playing. I've tried clearing the cache, logging out and back into Spotify, and restarting my device and nothing has fixed this. Any other suggestions would be appreciated.