Makefile.deprecated is no longer maintained or even tested since 2013 - now there is a new makefile and a CMake build. The old file was originally left as reference, if something is not working with the new build - and then forgotten.
I have no experience with cygwin - for Windows there is a Visual Studio build and a MinGW build.
But, if I got it right, the CMake file works for cygwin, so maybe it's time to get rid of this old, unmaintained Makefile.