Mouse cursor won't move

I just bought Impossible Creatures from gog, and after launching it, I noticed the mouse cursor wouldn't move. It remains visible at the center of the screen, but simply won't move, no matter what I do with my mouse.

Interestingly, it seems that it is only the cursor that won't move. The buttons still highlight when the mouse hovers over them. In other words, I can still click around, but I can't tell where my mouse is, until it hovers above a button.

Basically, the game is almost unplayable, since I have no idea where I'm clicking. At best, I can tell if my mouse is hovering above an enemy unit by looking at how the cursor changes, but I can't tell which unit I'll be attacking if I click.

How do I fix or work around this issue? I'd be happy enough, if I could just prevent the game from hiding my regular mouse cursor.

I'm on Windows 10, with all updates installed including the major November update. I've tried running the game as administrator, and even in Compatibility mode for Windows 8, 7, and XP SP2 with no success.