Something is wrong. You cannot have BOTH a g41 and a g31. I suspect a documentation error in the first image.
Now, are you asking about an update for windows 10? If so, windows 10 is not supported on either chipset.
Download and run this utility, then attach the results.
https://downloadcenter.intel.com/download/25293/Intel-System-Support-Utility Download Intel® System Support Utility for Windows*
Then, an Intel support engineer will be able to assist you.
You should note that the g41 and g31 are from 10 and 11 years ago. Hardly capable of the requirements of today's games, and no update will make it any better. This also means your hardware (motherboard, processor) is 10 years old. The best option is for you to get a new(er) system that is supported and has the graphics support you need.
The first image is a snapshot of the pdf of the motherboard's specs. You said that it is not possible to have bot g41 and g31, but that's what i have, and i don't want to update for windows 10.
I don't want to play today's games, i play old games like COD 2 , Halo CE, POP two thrones, etc.
Ok, just because the motherboard specs say you have a g41 does not mean it is correct. Like I said, it is likely a documentation error, or you are looking at the documentation for a newer revision of your board.
Run the utility as I asked, and attach the results.
Until we know for certain what you have, we cannot provide an update.
Also, as I said, an update is really not going to make a difference on a platform this old.
As I suspected, you have a G31.
Here are the drivers for your graphics: https://downloadcenter.intel.com/product/81520/Graphics-Drivers-for-Intel-G31-Express-Chipset Downloads for Graphics Drivers for Intel® G31 Express Chipset