Try setting "Engine Id" to "4" and "Screen Hardware3D" to "0" like described in this thread. It's important not to run the game as another user, e.g. as administrator or in compatibility mode, because the registry key won't have any effect then. Just double-click DKII.exe within the \Dungeon Keeper 2\ folder.

The game also depends on some older libraries from DirectX 9, which are missing by default on Windows 7 and newer machines. To make sure everything is present on your system, you can download the DirectX End-User Runtimes and install it. When you run the downloaded file, it asks you where to extract the files. Choose a separate folder, as there'll be many files and afterwards look for dxsetup.exe within this folder to start the installation.