The image size of a video game depends on 2 things.
- The graphics card.
- The monitor used to see the image.
The monitor can be irrelevant at some point. You can turn it off and still press the "print screen" key to put the image in the clipboard. But you still need to tell the resolution of the game output and the best way to do it is using a monitor with that native resolution.
As far as I know, on a gaming console, you need to take the output feed on an external device parallel to your TV to capture the footage (probably using a computer again)
Regarding the print size, you can print it any size you want. 20x30 inches? sure... The catch is that you need to define the internal resolution and detail you need, and this is given by the viewing distance.
One way to think about this case will be thinking about your print size the same size as a monitor. 100PPI is a good print resolution.
Let me make you a random table of the resolution of monitors in:
Diagonal inches - resolution - PPI value
Inches resolution px PPI
24 FullHD 1920x1080 92
27 Quad 2560x1440 109
40 4k 3840x2160 110
If you print an image of a 4k monitor on a paper 30inches long, the resolution is simply 3840/30 128PPI.
It is not perfect, but depending on the image, it is good enough as it is, or you can simply resample it, let's say double the resolution to get 256PPI.
Do you own the image?
The screen capture? Yes, you "own" it. You can use it as your computer wallpaper, or print a mug for your kids if you want.
But the content of the image is not yours. It is a screen capture of a video game, this means basically that you can not distribute or make any profit from it.
If what you want is to have apocalyptic cityscapes, the best thing you want to do is learn how to make them, basically learn 3D software.
Your best option is probably Blender and or Unreal Engine, both free and both with very interesting options for what you want.
But it is not a speed race; it is more like a marathon.
P.S. I am not sure the correct term is "virtual photography" it is more like "virtual image" or the most used term... CGI. Computer generated Image.