Different Strokes.......
Game background seems like it would be done in different ways. If you look a something like "Spider Solitare", it works at any resolution you might set. This is because the background is merely a fill layer of textured green and Windows knows which monitor resolution is currently set. The cards are actually small windows and display at the same pixel dimensions irregardless of the screen settings.
Now when you deal with a game, which is actually a bit mapped scenery, the game itself would have to describe a larger section of the scenery file to the OS for display. A building might come into the picture, not simply a repetitive background texture.
When you deal with an imaging program, such as Photoshop Elements, one of the preference options is "allow pictures to resize". If this is checked, then the image will appear full screen, well "bigger" as it applies to the original complaint in this post. This would be because a picture say 300 X 400 pixels would now be 600 X 800, with each line of the original image now covering 2 lines of the monitor's screen, with the image now being twice the linear dimension and 4 TIMES the area.
So, unless you're prepared (or able) to modify the programming in the way I suggested above this discussion is somewhat moot.
I have a small number of games that I would like to appear on my new 22" at it's native 1680 X 1050 resolution. Unfortunately, they were written sometime ago, and I take what I can get.