Bingo! Then I believe it is (at least theoritically) possible to treat a game's 2D screen as a big rectangular polygon, and then applying texture scaling/filtering to the 2D screen.
This is exactly what I DON'T want to do. By doing that, you'd lose every information about depth, and that means no stereoscopy support. Moreover, everything would end up looking either messy and blurry, or extremely pixelated, because you would have just enlarged a 2D image, as opposed to natively display a 3D scene at a certain resolution.
The following is an example of what I mean.
This is a screenshot of a game running at a native resolution of 1024*768.
This screenshot was originally grabbed at 640*480, then upscaled to 1024*768 with a bilinear resample effect.
This is another screenshot that was originally grabbed at 640*480, then upscaled to 1024*768 through a simple pixel resize.
Technically, all three of them have the same resolution, but the first one is much more detailed and crispy, because it was not treated like a 2D image: the 3D scene was actually displayed at that resolution.