/usr/include/gnome-desktop-3.0/libgnome-desktop/ is in libgnome-desktop-3-dev 3.8.4-0ubuntu3.
This file is owned by root:root, with mode 0o755.
..
/usr/include/gnome-desktop-3.0/libgnome-desktop/gnome-bg-crossfade.h
/usr/include/gnome-desktop-3.0/libgnome-desktop/gnome-bg-slide-show.h
/usr/include/gnome-desktop-3.0/libgnome-desktop/gnome-bg.h
/usr/include/gnome-desktop-3.0/libgnome-desktop/gnome-desktop-thumbnail.h
/usr/include/gnome-desktop-3.0/libgnome-desktop/gnome-idle-monitor.h
/usr/include/gnome-desktop-3.0/libgnome-desktop/gnome-languages.h
/usr/include/gnome-desktop-3.0/libgnome-desktop/gnome-pnp-ids.h
/usr/include/gnome-desktop-3.0/libgnome-desktop/gnome-rr-config.h
/usr/include/gnome-desktop-3.0/libgnome-desktop/gnome-rr.h
/usr/include/gnome-desktop-3.0/libgnome-desktop/gnome-wall-clock.h
/usr/include/gnome-desktop-3.0/libgnome-desktop/gnome-xkb-info.h