So I thought, hey, it's just a matter of swapping stereo channels, right? There ought to be something like that in the driver settings or in Windows 7 control panel, or registry or somewhere! As it turned out, Windows used some built-in drivers for my on-board Realtek HD Audio card, and Windows 7 itself doesn't have the "reverse stereo" option. Well then, I must install Realtek drivers and there I'll find what I need. Or so I thought.
After installing Realtek drivers, I ended up with some crappy Manager in my tray, which had ridiculously many settings, including type of material that walls in my room is made of. But no "reverse stereo" option, of course. I should've guessed. There is no way hardware manufacturer will provide anything useful in their software except maybe drivers. If it was Linux, I know I could've done it with some ALSA settings, but I just didn't want to install Linux just to play a single Windows game, even though it's supposed to run there with no problems.
Now stupid people (or people assuming that I'm stupid) would say, "Hey, how about just moving your speakers?" Duh! If it was so easy, I would've done it when I was placing them there in the first place. The reason I couldn't do it was that the AC cable is too short to reach the place where the right speaker is, so I just had to place it on the left side. And no, using an AC extension cord is not an option: I don't want to increase the number of 220V cables and plugs around my PC more than I have to.
So I had to look for hardware solution for the audio cables. I didn't want to rewire cables manually, though. It turned out to be pretty simple:
After plugging these two beauties into each other, we get this:
Now it is possible, by swapping RCA plugs, to either reverse stereo or restore it back. But really, it's the first time I had to solve a software issue in a hardware way.