I see no reason for the ground wire.
In the case of a piece of audio equipment that does not use the wall receptacle safety equipment ground, if the equipment was designed properly the signal ground of the piece of equipment is connected to the metal chassis of the equipment.
A piece of audio equipment where the equipment is designed to use the wall receptacle safety equipment ground the designer of the equipment may have or not have connected the circuit signal ground to the metal chassis of the equipment. Some designers incorporate a switch so the user can lift the signal ground from the wall safety equipment grounded chassis.
When an interconnect is connected between two pieces of equipment the signal grounds of the equipment is connected together by the signal ground return wire of the interconnect.
Any time a piece of equipment that uses the wall receptacle safety equipment ground, where the circuit signal ground of the equipment is connected to the metal chassis, and then connected to a piece of equipment that does not use the wall receptacle safety equipment ground, that piece of equipment also then becomes grounded to the wall receptacle safety equipment ground by the signal ground wire of the interconnect.
I suggest you look for another interconnect manufacture.