Note: This works for me, I don’t have your computer, I have my own, so ymmv.
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Grab two files:
http://sourceforge.net/projects/mingw-w64/files/External%20binary%20packages%20(Win64%20hosted)/MSYS%20(32-bit)/MSYS-20111123.zip/download
http://sourceforge.net/projects/mingw-w64/files/Toolchains%20targetting%20Win64/Personal%20Builds/mingw-builds/4.8.2/threads-win32/sjlj/x86_64-4.8.2-release-win32-sjlj-rt_v3-rev2.7z/download -
Extract these files where you like.
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Inside the new msys directory, run postinstall/pi.bat and answer the questions it asks. MinGW is installed in the mingw64 directory where you extracted the files before.
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Grab the ioquake3 source from github and extract it where you like.
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Create a file in the ioquake3 directory named Makefile.local. This file must have exactly one line in it:
WINDRES=windres -F pe-i386 -
Run msys.bat from the msys directory and change to the ioquake3 directory.
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Type make.
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Post here when something goes wrong.