Windows 10 should function with drivers from Windows Vista to 8.1, which is nice because Win10-specific drivers are almost non-existent right now. I would try the drivers at Intel® Download Center if you haven't already.
I should have said I tried to install the Windows 8 one and it wouldn't work (incorrect Windows version was the message I think). I also tried in compatibility mode with the same error
It seems Intel's GPU driver installers have become a lot more picky about the installation environment than they were in the past. I can install drivers for 15-year-old GPU's onto Windows 7 just fine (although OpenGL doesn't work and they're slow; the latter is obvious) and run Windows 10 on a GMA 950. That being said, I have experienced this problem before on other people's machines with various HD Graphics processors. I believe it's possible to extract the contents of the installer using Universal Extractor or something similar (maybe 7-zip?) and then using Device Manager to install the driver, but I've never actually tried it, as I don't have a need to with my current hardware.
EDIT: D'oh! I didn't realize there's a zip driver provided, so no need for Universal Extractor. You can get the zip file at Intel® Download Center. If installing it via Device Manager doesn't work, then either the drivers are not properly signed and you need to temporarily disable driver integrity checks, or it's just not going to work.