This file is indexed.

/usr/share/desktop-directories/Game.directory is in gnome-menus 3.13.3-6ubuntu3.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

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[Desktop Entry]
Name=Games
Comment=Games and amusements
Icon=applications-games
Type=Directory
X-Ubuntu-Gettext-Domain=gnome-menus-3.0