The store page said this game works on Windows XP.

But the version 1.2.0-5 that is available right now does not work due to Vista-only imports:
AcquireSRWLockExclusive
EnumSystemLocalesEx
InitOnceExecuteOnce
etc.

Was there an older version that worked? If so, how can I download an older version?

I’ve read that some users were able to request an old installer (for a different game) talking with GOG support. But I can’t tell you a version of CrossCode that worked with XP.

In any case you don’t loose anything to ask them about it.