My memory of it is that you can use key commands to save the game. I can't remember what they are exactly. Sorry!
A modern fix for this would be to use AutoHotkey to create a script where, if you had the 'cursor stuck on the left' bug happen, you could fire the script and have it trigger mouse-clicks at the screen positions needed to save your game. Very simple to do something like that.
Or by what Graccio said above, perhaps the script could fix the bug by rapidly moving the cursor to the left?
Gracchio: I took a look at it because Dungeon Keeper is one of my favorite games of all time.
The game runs in a small frame which is stretched over the entire screen. However, the mouse area is also stretched. When you go to the left, you meet a wall where the value cannot become smaller, 0. When you go right, the mouse location coordinates simply becomes a number greater than the maximum size of the variable that holds the mouse position value so it loops around and voila, your mouse is stuck to the left. Look up calculating with binary if you're curious about how the looping works.
Workaround: Use your arrow keys to move. If you do get stuck, start dragging your mouse to the left.
You can clearly see this happen if you alt tab out of the game and drag the cursor to the far right of your screen.
Interesting to finally understand why this old bug happened! Thanks for the info.