I can't find what the arm looks like, but it says patent pending...so go search up their patent.
EDIT: I see the video. That's just a pulley with a motorized knobby thing to go into the center of the CDs and become wider to grasp it. It's also not resistant to sway, it's just that the gripper at the end fits into a shaped slot when it's fully retracted so it's not actually free swinging.
And why do you need copper cord? To send signals and power to the gripper at the end? You could just make a separate "coiled" telephone type cable to send power and signals with a separate cord for the pulley. Would work just fine...
Also, notice how wide the robot is, and how the cord is almost the same length...it may not be wound up inside at all, but just being pulled back and forth on a rack.