Yes, in addition to the audio signal, electrostatics require a high voltage to energise the stator panels which form part of the driver system that make the sound.
That high voltage has to come into the headphones via the cable from the Stax energiser box. So the cable has to have additional wires to carry the voltage.
Here is quite a good article explaining the different headphone driver types...
We’re here to give you a breakdown of four different driver types: dynamic, planar magnetic, electrostatic, and balanced armature drivers.
www.soundguys.com
"Electrostatics operate on a completely different principle than the conventional dynamic technologies discussed. They work by applying a static electrical charge to a thin film that floats between two perforated metal plates; when audio signals are applied across the plates, the entire film membrane moves back and forth due to electrical attraction and repulsion. It’s the same principle as
condenser microphones use to capture sounds but in reverse.
Wikipedia Commons With electrostatic drivers, the diaphragm is propelled to and from a pair of surrounding metal plates.