how do I make Drupal Zen sub theme mobile friendly?
I have just checked the Superfish project status and there are bug reports that Superfish breaks with jQuery versions 1.9 and above. Check what version of jQuery is loading and check if there are any Javascript errors in your browser console.

If that is the problem, you may have to wait for the next version update, or roll back to jQuery 1.8 for the time being.

Superfish jQuery 1.9 Bug Report