While it's an old topic, I wanted to play this game again, and I had the same issue - as in I wanted to run this in windowed mode. Couldn't find the solution anywhere, but I managed to get it working myself with DXwnd, so if anyone stumbles across it, here is how I did it (I am on Windows 7 64 bit).
You have to set both game.exe (note - it's game.exe in the ~/Desperados/Game/ subfolder, and NOT the Desperados.exe) and DXwnd itself to run as an administrator, also set game.exe to run in compatibility with Windows XP. Make sure the window size in DXwnd is correct (so probably 1024x768). Side note: if you are messing with the settings in DXwnd, remember to kill the game.exe process in task manager if it is running, otherwise the game won't start.