Where does your msysgit.bat come from and what is its content (code) ?
I assume it opens up a bash-like MinGw shell under windows with git commands available. For calling a command such as git mv /e/buildUFOAI/ufoai/base/maps/city_industry.map /e/buildUFOAI/ufoai/base/maps/industrial/ind_city_industry.map from a cmd command window, or a batch script, or a python script, you would need to have msysgit installed with git command known to the system via environment variables. Or alternatively, use a full path to git.exe.
e.g. something like (in batch)
cd C:\ufoai //with ufoai being the project root, contains .git folder
C:\Program files\Git\bin\git.exe mv base/maps/city_industry.map base/maps/industrial/ind_city_industry.map
I'm pretty sure that this would about work on my windows system, where I have the former version of
https://git-for-windows.github.io/ installed. And writing a script doing it shouldn't be very difficult. (I can't compile UFO:AI on windows but git operations work, on the same checkout.)
EDIT
I just checked that it indeed works in cmd.exe:
F:\ufoai>i:\programs\Git\bin\git.exe mv TODO DONE
renames the file like it should.
Which surprises me, since normally I do git operations on windows also in a MinGw-like shell, which was added to the explorer's right-click menu by installing git.