Sometimes apps downloaded from the web can be enclosed in quarantine.
Quarantine is an ancient technology implemented by Apple to protect Mac OS X, but sometimes it can lock "friendly" apps without any interaction with user.
If nothing happens when You click "Sign In" in button in VOX for Mac - first of all, check the VOX Cloud icon in menu bar. If it's not there, it might get into quarantine.
To remove the VOX Cloud from quarantine You need to close the VOX app and enter three commands in terminal one by one.
Don't forget to wait few seconds for a command to be executed.
launchctl remove com.coppertino.VOXCloud
sudo xattr -d -r com.apple.quarantine /Applications/VOX.app
Enter user password and hit enter
/System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.framework/Support/lsregister -kill -r -domain local -domain system -domain user