Since \"gcc -mno-cygwin\" does not work anymore, I was looking for a way to get a MinGW-targeted GCC running within my Cygwin environment. (Running a MSYS environment is not
Cygwin homepage says that "Individual packages like bash, gcc, less, etc. are released independently of the DLL.".
Here you can find how to install gcc under cygwin, so you should also select gcc package during install not only gcc-mingw.