The jack plug of the headphones is a 3.5 mm stereo jack plug with a 6.3 mm adapter. This 3.5 mm plug always fits into the HyperX QuadCast, as the microphone supports a 3.5 mm headphone connection. This means you can connect the headphones directly to the HyperX QuadCast.
The headphones have a cable with a fixed 3.5 mm jack plug and a screw-on 6.3 mm adapter that can be removed if necessary.