Your Turtle Beach PX22 are USB - correct?
The red and white are RCA stereo audio outputs.
You need to convert from a USB male to RCA via an adapter cable.
For example:
http
/www.ebay.com/itm/HDE-3-RCA-to-USB-Audio-Video-A-V-Camcorder-Adapter-Cable-for-TV-Mac-PC-USB-3-0-/122004512106
Most of the adapters I could find were all USB as is the example. However the cable comes with a gender changer.
You would just leave the yellow plug free.
Could not see any pinout diagrams that would confirm the connectivity you need. Especially if there is some proprietary connectivity being used.
Check the return/refund policy just in case.