Hm. There’s been an update on the situation.
Like Cliffski suggested, I lowered the resolution, turned off full-screen, and set “Processor Affinity” to only one core in Task Manager. It helped. Game speed now appeared to be back to normal - at least, back to how I remember it. However, when I left the battle and turned full-screen back on, the problem was back - when I entered the Tutorial level again, everything was back to going high-speed.
After some more testing, it turned out that it didn’t matter at all how many cores the game was set to run on - it could be only one, it could be all of them - all that mattered was whether I had the game running in full-screen! Windowed, it would run at normal speed; full-screen, it would run at exaggerated speed. Right now, I’m running the game windowed, but the resolution is set to the max. As such, the game looks exactly like it’s full-screen - you can’t tell that it’s actually windowed - but that doesn’t matter, because since the computer doesn’t consider it to be in full-screen mode, the game runs just fine.
So I guess we’ve found the cause of that problem, at least.