According to the requirements stated on the GOG page of IG2, the game ought to run on an XP PC with 2 GHz, 2GB RAM and an Intel 965 card. But it doesn't - "ig2.exe is not a valid 32bit application."

An explanation might be that IG2 also requires OpenGL2.0 support - as stated on the Steam page of IG2.

Has someone else made similar experiences, or, more importantly, an idea how to solve the problem (other than telling me to use a different OS or graphics card)?

I still have the original 4CD version of IG2, which does work on said PC. It looks like IG2 was tweaked to run on modern PC's, but sacrificing backward compatibility. How about offering the original version of IG2 (talking about "good OLD games"), too?

https://www.gog.com/forum/general/gog_installers_and_win_xp/post12

Thanks. It's perfectly legitimate not to support XP anymore, in my mind. But it's not ok (to avoid stronger words) to list XP as a requirement (see IG2's GOG product page) when the game isn't compatible with XP.
It would only be fair to offer the old XP compatible version of IG2 to customers who spent money for IG2 in good faith it would be XP compatible as announced on the product page.
Well, it's GOG's decision. But it's my decision which game portal I use ...

It is possible to get around the first problem ("ig2.exe is not a valid 32bit application") by hex-editing the IG2.exe executable (specifically changing the OS requirement flags) but that just results in a second error "The procedure entry point SetProcessDPIAware could not be located in the dynamic link library USER32.DLL".

So this requires work from the developer to fix this - I've raised a ticket with GOG support but aren't expecting much.

Well, it's been a while but I managed to find a solution to get the current version of IG2 running on Windows XP.

Details:
ig2.exe will need modification - to do this, you will need a hex editor - if you do not have one, I would recommend downloading and installing the free HxD.

Next, download the file userxp.dll (to provide the SetProcessDPIAware function) and place it in the IG2 folder
(the prudent may wish to check this file with VirusTotal to confirm that it is clean).

(edit: removed unnecessary reference to zlib1.dll).

Make a backup copy of the ig2.exe file (HxD will make backups by default, but best to take extra care).
Now use HxD (or your preferred hex editor) to edit ig2.exe to do the following:
1). change the system requirements flags by altering bytes 168 hex and 170 hex from 06 to 05 - see first screenshot.
2). change the host DLL for SetProcessDPIAware from User32.dll to UserXP.dll (bytes 4DA9F2 and 4DA9F3 - doing a search for "SetProcessDPIAware" should be the easiest way to find them) - see second screenshot.

Run ig2.exe and it should now work. Thanks to the Xompie website for the DLL which was able to do what THQ Nordic could not.