While technically correct, there would be enough delay/lag as to likely render many games difficult to play.
There's going to be no good way to connect a XDR display to anything but a modern Mac. It'll apparently work via USB-C off a current generation iPad Pro, but not sure if this is because the monitor supports USB-C video (obviously not at 6K) or if Apple specifically added support for the iPad Pro to the monitor.
If there's no DisplayPort output, then you need an HDMI to DisplayPort converter ($200 for HDMI 2.0 4K60, $60 for HDMI 1.4). I don't know if this will work with the PS4 or PS5 and the XDR. I did get 1080p from a PS4 through an HDMI 2.0 to DisplayPort adapter to a normal DisplayPort display (the PS4 only supports 1080p, need a PS4 Pro for 4K).
This cable outputs high-resolution video from any USB-C or Thunderbolt 3 computer like a MacBook or MacBook Pro and displays it on DisplayPort monitor. Supports up to 5K resolutions at 60 Hz.
People have successfully tested the following: the XDR display works from the USB-C (not Thunderbolt) port of an Nvidia RTX 2080 card in Windows and from a DisplayPort port (no USB) with the Moshi cable.