Hello Sebastien,
It is a Windows/Mingw-w64/MS-MPI installation. Visual Studio with Intel compilers and MS-MPI is a more common combination and it would have been more straight forward.
MPICH2 is also more compatible with mingw-w64, whereas MS-MPI is 'tuned' for Intel compilers. But its development for the Windows platform is taken up by Microsoft and MS-MPI.
Compilation of MUMPS and its prerequisite libraries was done within the new MSYS2 environment, which is a lot better and simpler than cygwin or MSYS. Compilation is based on the linux makefiles with minimal tweaking.
Regards,
Costas