The game refuses to start on my system Windows XP-64 SP2, stating that it will only run on Windows XP SP3. XP-64 is basically a Windows 2003 Server and unlike XP-32, my system can only use service packs from Windows 2003 Server (so SP2 is the last service pack that will ever be available).
IMO, the difference between XP32 SP3 and XP64 SP2 should be minimal and it must be just a trivial check that prevents the game from running on my rig. Should I bother devs with the question or just leave it and wait for some free time to upgrade to Windows 7?

Sigh... :-\
Yeah, I know I have to upgrade, but I thought maybe for the sake of another stubborn sob like me I'd push it a bit...
And I've just found that it's GOG Galaxy that's not starting not the game, the game runs fine...

FYI, Windows XP-64 is not a GOG supported Windows platform for anything. The differences are also nontrivial between them.

Honestly it's a first time I've encountered any difference and to be even more honest I've dug Galaxy executable a bit and it really seems like a simple check (or a number of checks). I've patched it and it worked (logged in at least) until updater service restored the correct executable. This understandably was the end of my journey to the great unknown. The Galaxy code looks pretty mature in the regard of handling updates. Hopefully if will also be stable enough.

Windows XP 32bit and 64bit were, unlike its successors, very different operating systems with a completely different kernel and core. They were "the same" in name only and differences were everything but minimal.
XP x86-64 was not based on the XP kernel, but rather the Windows Server 2003 kernel instead. It was also structurally different from future Windows 64bit systems.

But none of that should matter much, the OS is dead and unsupported and should no longer be used with online connectivity.

Well, there is no real difference between them as far as WoW-64 emulator is concerned. Kernel and drivers are different but what's going on in kernel should stay in kernel. All in all it's a perfectly compatible Windows XP 32 emulator on Windows 64 platform.
As for 2003 being dead, well... I'm still using it (32 and 64) on all my servers at work (there are around 40 in three cities). They are licensed as a downgrade from 2008/2012. And I currently see no reason to upgrade to 2008. Servers are a different kind of lot. A server often needs only LAN card drivers to function properly.

Why do we converse in this dead thread anyway? ;-)