Okay, I'm not an expert, but I have an idea...
It looks like your graphics card is rendering the model wireframes for some reason. You said that this is a screenshot, so that would indicate to me that this is being pulled directly from the graphic card's memory, which gives me the impression that there's nothing wrong with your display.
If this happens more consistently with 3D games than with 2D games then I'm also getting the impression that you might have a corrupted runtime library(s) associated with graphics rendering somewhere. That's generally bad news, but it is fixable.
I don't know what that hypothetical library(s) could be, but you might be able to find some specific result if you look at all of the files opened by each game that's malfunctioning and find the file(s) that all of them have in common.
You should be able to re-install those files and get the games to work.
However, since I'm not an expert, I would recommend that you show this problem and potential solution to someone who's proficient (to say the least) with troubleshooting these kinds of errors.
TL;DR Talk to an expert.