Concerning ownership and usage of the image, that’s a question that is better asked of a lawyer in your jurisdiction. The IANAL version is a pretty firm “yes” under (most) western copyright law, but with the caveat that under that law, whether you can display, sell, or otherwise distribute the image falls somewhere between “no” and “maybe” depending on many factors including, but not limited to, the specific laws for producing derivative works in your jurisdiction, fair use law, all that EULA text you agree to by playing the game (on a per-game basis), and a few hundred other considerations.
Your resolution limit will be what the graphics card is set to render, so I’ll assume 4k rendering: 3840 × 2160 image (8.2mp) at a 16×9 ratio. Of course, if you’re dealing with 1920 x 1080, divide all the final numbers by 2 below. Also, this assumes the games allow you to take the images at the full screen resolution.
The biggest limiting factor will actually be the resolution of the art assets in the game.
You might be able to crank the resolution up to 8k on some games, but it’s entirely possible the textures used will not hold up at that resolution. You want to essentially shoot landscapes, so a lot will depend on if they are accomplishing the appearance of distance by using ray tracing to render atmospheric effects on a distant object, or if they are simulating it by having a closer object with those effects pre-rendered on the texture.
Basic Print Size Math
Generally speaking, the human eye has an angular resolution of about .0003 radians, so for any distance, the smallest object the eye can perceive as a unit is
0.0003d for any distance
d in any unit you care to use.
So we can plug in a viewing distance of 1 meter and get a resulting maximum pixel size of 0.03cm or about ≈33dpcm(≈84dpi). Because our visual acuity won’t always line up perfectly with a grid the same size as our eye can see, this will generally look “soft” or “jagged” to us (depending on how clean the pixel edges are printed), so the general rule of thumb is based on rounding up and doubling these numbers, so 70dpcm or 180dpi at 1 meter viewing distance. (This is also why you can “get away” with using a slightly lower resolution if you use a medium that has a softer edge than an inkjet printer might have, like an optical printer on silver halide paper.)
So at a 1m viewing distance, a 4k image can be reasonably be printed on an ink jet printer about 30.8 x 54.9cm or 12 x 21.3in. You might be able to get away with a 20×30 if you use a silver halide process, but it will likely be a bit soft.
All of this scales linearly, so if a print that size is smaller than you’d like at a distance of 1 meter, you may not be entirely happy with the results.