UPDATE: Problem solved (kind of)

So I found a way that fixes the symptoms. I'm not sure how it "just worked" before, but if you have the same problem as me, here's what I did.

My graphics driver is from Intel. So I downloaded the appropriate intel control panel (not just the driver -- this also included a program with additional configuration options), and I turned on scaling that way.

I encountered the same problem, not just with the GOG version, but some years ago on another computer. You must be very careful when you start the game for the first time. You will once, and only once, be presented with a box with a little square that you can tick, which allows you to switch to game resolution when starting the game. Make sure you opt to switch to game resolution. Also, I think once inside the game you can go to the preferences part, where you can choose such things as whether to fight your battles or let the computer mangle and lose them for you. I think there is a an option there as well to switch to game resolution.

I hope this helps.
I just fired up the game to refresh my memory. From within a running game, go the "game controls" square on the top right of the page, then choose "preferences." Under the battles option there is a choice for resolution. I have never clicked on it, as I do not wish to risk messing up what is now a perfectly running game, but I see no reason why that should not fix the problem.

Game has never launched to allow this option.