I have solved the problem. Thanks a lot!
Thanks this helped a lot to debug. In VLC when I pressed the Start button to start playing music the following error appeared in the console:
http stream error: local stream 1 error: Cancellation (0x8)
Then I have searched the web with above error and found the following thread on official VLC forum just few days old with suggestion:
Tools → Preferences → Show settings: All → Input/Codecs → Access modules → HTTPS → uncheck Cookies forwarding
Saved the setting and restarted VLC. This solved my problem. Now I can play music from VLC just fine.