/usr/include/mate-desktop-2.0/libmate-desktop/ is in libmate-desktop-dev 1.20.1-2ubuntu1.
This file is owned by root:root, with mode 0o755.
..
/usr/include/mate-desktop-2.0/libmate-desktop/mate-bg-crossfade.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-bg.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-colorbutton.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-colorsel.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-colorseldialog.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-dconf.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-desktop-item.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-desktop-thumbnail.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-desktop-utils.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-desktop.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-gsettings.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-rr-config.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-rr-labeler.h
/usr/include/mate-desktop-2.0/libmate-desktop/mate-rr.h