Hey, the WineD3D solution in this thread helped me, but the posts here were really confusing! I'm posting this to try to clarify for anybody having the same problem. Part of the problem is that GOG doesn't seem to want anybody posting links on the forum, so I'll try to work around that maybe somehow?
* Download wined3d.exe from: nongnu (dot) org (slash) wined3d
* The DLLs are kind of hidden away inside the installer. You'll need 7zip installed to get to them (also free and open source) available from: 7-zip (dot) org
* Go to the folder where you saved wined3d.exe; right click on it, go to the 7-Zip sub-menu, and select "open archive".
* In the new 7-zip window, go into the "$SYSDIR" folder, where there are lots of DLLs and other files. You only want three of them.
* Copy "wined3d.dll", "libwine.dll", and "ddraw.dll" into your arcanum directory. (This is the same folder that has Arcanum.exe, and might be something like "C:\GOG Games\Arcanum\"). You can simply drag-and-drop them from the 7-zip window to your arcanum folder.
* Tell it to replace existing files, namely the original ddraw.dll (or you could move or rename the original ddraw.dll if you feel like it)
* Start the game and it just might run a lot smoother now! It worked for me at least.
(Obviously you should only attempt this process if you're comfortable doing so; worst case scenario, you might need to reinstall Arcanum if something really strange goes wrong. Attempt at your own risk, not reviewed by the FDA, for external use only, and so on)