dick1982: it just gives me a black screen
Well, it is a tech demo, so there was no compatibility testing done for it (GOG added a readme file stating it wouldn't work on some systems).
Try right clicking on the LMK.exe file and running as administrator, or right click, select Properties and switch to the Compatibility tab, and try different options there (compatibility modes, disable display scaling on high DPI settings, etc).
I just reinstalled the demo (as administrator, to d:\games\LMK, though the location shouldn't matter), and had no problem. It should load straight into the game, with the screen centered on the character...
If you have a mouse cursor, is it changed to the game icon?
Do you see or hear anything if you click and hold the left mouse button down? That should move the character, and if necessary recenter the screen focus on him.