The PATH environment variable is the search path for executables, not for other kinds of files. For include files, you need to arrange to pass the option -I/usr/include/gtk-3.0/gtk to the compiler. Typically, you do that by setting a variable defined by a makefile (usually CFLAGS='-I/usr/include/gtk-3.0/gtk'), or by passing an argument to ./configure (typically ./configure --includedir=/usr/include/gtk-3.0/gtk).
With Gtk and other software following Freedesktop practices, the proper way to indicate the location of include files, as well as other compiler and linker options, is with pkg-config, as described in Celada's answer.