The one downloaded from this link:
http://sourceforge.net/projects/ufoai/files/UFO_AI%202.x/2.3.1/ufoai-2.3.1-win32.exe/download
It doesn't seem to work, and I have no idea how to compile/run the 64 bit version, or where to start with it anyway.
Can you please elaborate on "It doesn't seem to work" a bit, such as the exact error message you are getting (screen shot? log?), or exactly what doesn't seem to work right?
I have several computers I multi-boot with various operating systems of different versions, between them I have several installs of Windows 7, one 32-bit and two of them 64-bit, and I've run this game on the 64-bit installations of Windows 7 without ever having any issues related the version of Windows. To be fair, I have several programs and apps that won't work on 64-bit Windows as they insist on only working in a 32-bit environment, but the vast majority of my programs and utilities work in 64-bit Windows regardless of what type of Windows they were compiled and built for.
Also, can you please tell us if you are running a "true" Windows installation or a virtual/shell environment? In my experience sometimes running Windows within a special non-native environment can cause compatibility issues.
IIRC the installers on Sourceforge may have been cross-compiled from Linux, which sometimes causes things to go wrong, but I haven't seen this issue come up before.
I'll download and double-check the installer myself anyways though.
BTW, I've actually been trying for some time to build a 64-bit compiled version of the game, using MinGW-w64 toolchain, although I've had limited success as it seems to almost but not quite fully work. It isn't a developmental priority for me at the moment though, as I need to finish up something else in the code before I really get back to such an experiment.