/usr/share/desktop-directories/ is in kde-runtime-data 4:15.12.3-0ubuntu1.
This file is owned by root:root, with mode 0o755.
..
/usr/share/desktop-directories/kde-development-translation.directory
/usr/share/desktop-directories/kde-development-webdevelopment.directory
/usr/share/desktop-directories/kde-development.directory
/usr/share/desktop-directories/kde-editors.directory
/usr/share/desktop-directories/kde-edu-languages.directory
/usr/share/desktop-directories/kde-edu-mathematics.directory
/usr/share/desktop-directories/kde-edu-miscellaneous.directory
/usr/share/desktop-directories/kde-edu-science.directory
/usr/share/desktop-directories/kde-edu-tools.directory
/usr/share/desktop-directories/kde-education.directory
/usr/share/desktop-directories/kde-games-arcade.directory
/usr/share/desktop-directories/kde-games-board.directory
/usr/share/desktop-directories/kde-games-card.directory
/usr/share/desktop-directories/kde-games-kids.directory
/usr/share/desktop-directories/kde-games-logic.directory
/usr/share/desktop-directories/kde-games-roguelikes.directory
/usr/share/desktop-directories/kde-games-strategy.directory
/usr/share/desktop-directories/kde-games.directory
/usr/share/desktop-directories/kde-graphics.directory
/usr/share/desktop-directories/kde-information.directory
/usr/share/desktop-directories/kde-internet-terminal.directory
/usr/share/desktop-directories/kde-internet.directory
/usr/share/desktop-directories/kde-main.directory
/usr/share/desktop-directories/kde-more.directory
/usr/share/desktop-directories/kde-multimedia.directory
/usr/share/desktop-directories/kde-office.directory
/usr/share/desktop-directories/kde-science.directory
/usr/share/desktop-directories/kde-settingsmenu.directory
/usr/share/desktop-directories/kde-system-terminal.directory
/usr/share/desktop-directories/kde-system.directory
/usr/share/desktop-directories/kde-toys.directory
/usr/share/desktop-directories/kde-unknown.directory
/usr/share/desktop-directories/kde-utilities-accessibility.directory
/usr/share/desktop-directories/kde-utilities-desktop.directory
/usr/share/desktop-directories/kde-utilities-file.directory
/usr/share/desktop-directories/kde-utilities-peripherals.directory
/usr/share/desktop-directories/kde-utilities-pim.directory
/usr/share/desktop-directories/kde-utilities-xutils.directory
/usr/share/desktop-directories/kde-utilities.directory