I think this project isn't supporting building with Mingw.
There are build instructions here for building with Visual Studio (which can be downloaded for free as the Visual Studio Express Edition from MS Website: http://www.visualstudio.com/en-US/products/visual-studio-express-vs
Build instructions here: http://cairographics.org/end_to_end_build_for_win32/
It's probably possible to make this work for MingW, but you will have to make it work yourself, which may be a bit of a long step for someone who is new to compilers and build scripts in general.