fisk0: Also having this issue, on a Windows 10 machine with a GTX 1050 TI.
I'm using a regular Microsoft Basic Optical Mouse, so it shouldn't be a mouse DPI issue either (I know modern gaming mice with DPI switches often cause problems in games from this era).
It seems like I'm actually moving a cursor around, but it isn't shown, as I managed to enter the settings menu at one point by moving the mouse around and clicking.
EDIT: I managed to get it working through these steps:
1. Go to the install folder (Galaxy has a shortcut under More > Manage Installation)
2. Right click Empires_DMW.exe and go to properties
3. Click the compatbility tab and the "Change settings for all users button" at the bottom
4. Check "Run program as administrator", "Disable full screen optimization" make sure "Disable DPI scaling set by:" is checked at set to "System (extended)" rather than the default "Program".
5. Apply and close the window and try launching the game again.
It's weird that we have to go through these steps since this is basically what GOG are supposed to do when they rerelease older titles, but I got it working through these steps.