REPOST from Reddit:
The reason this game doesn't work on Windows 10 and poorly on Windows 8, is the same old DirectDraw story.
TL;DR How to get the game to work:
Issue: Game shows 3 screens in low color. GOG has added a so called compatibility database to resolve some issues with the game like CPU process affinity. However, this database includes two entries ForceDirectDrawEmulation and ForceDirectDrawWait. These entries must not be set on Windows 8 or higher - in fact they are the ones responsible for the game not working at all. In order to fix this, you need to download the Windows 10 ADK. More specifically, you need the Compatibility Administrator (32-bit) from it. Open the file goggame.sdb in the WH40K folder, right click the WH40K.exe entry under CHAOS GATE and remove the aforementioned fixes. Save the file and install it to replace the already installed file. Alternatively: I've prepared the SDB file for you, and you can download it here. Open an administrative command prompt, navigate to the folder with that file and type sdbinst wh40k.sdb . Answer the question with yes.
Issue: Game freezes after trying to enter a mission. Do not rename the file as some people suggested in the forum. It's important that at least the GlobalMemoryStatusLie and SingleProcAffinity of the compatibility entry are affecting the game. See 1 on what to do, and keep the name as WH40K.exe
Issue: Game suffers from poor performance. Two options: You can use DXWnd to force WH40K.exe into windowed mode, that will fix the problem. In order to keep fullscreen working at decent performance, you need to use the NoGDIHWAcceleration entry in the compatibility database (set by default) and use dgVoodoo on top. Note that dgVoodoo will only work if you empty the compatibility modes of the database entry.
https://www.reddit.com/r/gog/comments/5g949o/16_months_ago_a_gog_rep_said_he_had_servitors/dargyiq/
Good luck to us all. I may come back to this at some time in my backlog of crap to deal with.