These are the steps I had to take to get the game to run:
1.) Install Arcanum to a folder in, or under, your home directory. e.g. C:\Users\Goger\Arcanum
2.) Delete ddraw.dll from the installation folder (or, to be safe, rename it to something like ddraw.dll.old)
3.) In the compability mode settings for Arcanum.exe, select "Windows XP (Service Pack 3)". Note that this will also make the game ask for administrator privileges upon starting.
This way I got the game to run. Scrolling the map results in some graphics glitches though, which disappear when I run the game with the "-no3d" commandline option.
Hope somebody else can use this.