It is possibly rendering the display of the virtual machine offline, and using screen recording to capture its output for display? Roundabout way to handle VM and virtual GPU that's detached from a permanent user interface window. Possibly the only way, I'm not sure.
Since somehow granting this permission was required to even make display work on older versions prior to it being designed to ask for it, it can be assumed that the GPU subsystem has always functioned like this, since before it was necessary to ask for and receive the Screen Recording permission.
The rendering issue was there in Mac OS Catalina. In BigSur, VM boots and renders fine, even if we don't allow that setting. So I think the only issue is that pop up shouldn't come at all. Anyways we are tracking it internally.