xdg-desktop-menu is not doing it right, or the documentation lacks.
I'm confused by the xdg-tools, like xdg-desktop-menu. It seems to install to /usr/share/applications by default. But sometimes this should be /usr/local/share one would think according to Linux standards.
Then there is also desktop-file-install, which can specify a DIR. It's not clear why there are two tools and which one to use when. So at least lack of documentation or clarity in the manpages I think.
Due to this, at least Processing and Arduino are now installing *.desktop files to /usr/share/applications, but that should be /usr/local/share I would think.