Why can't that OS be one of the standard ones?
Sure, it might require special hardware and software (even your screen has it's own software and processing that it is doing on the signals coming from your desktop), and at the end of the day the OS would need to change and evolve to handle this new paradigm, but it's not impossible to imagine a system where the "PC" does what it does now, and just tells the "VR" sub-processor/sub-machine where to put the rendered "window".
Already there are some VR apps that basically wrap your normal "windows" desktop in almost a cylinder around you and you can move screens around on it as much as you want with current VR headsets.