ArcGIS Server uses 64-bit python, not 32-bit, therefore, you need to install the 64-bit version of win32 on the server machine. To run the tool local, not published, you need to have the 32-bit version of the module. It's ok to install both the 32-bit and 64-bit versions of the same module on the same machine if you have both desktop and server installed because you have two seperate installation of python 2.7.x installed on that machine.
Let me know if installing the 64-bit version fixes your issue.