After successfully testing the 64 bit popcnt version in Arena (using wine in Mint 18.1), I tried the 32 bit version on a WinXP 32 bit computer.
It failed with the message about it not being a valid Win 32 application.
I then went back to my linux computer and ran the "file" command on it.
It gave the following result
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Fire_7.1_w32.exe: PE32+ executable (console) x86-64 (stripped to external PDB), for MS Windows
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Alaric707.exe: PE32 executable (console) Intel 80386, for MS Windows