I created a file named games.menu
with the following content:
<!DOCTYPE Menu PUBLIC "-//freedesktop//DTD Menu 1.0//EN" "http://www.freedesktop.org/standards/menu-spec/menu-1.0.dtd">
<Menu>
<Name>Applications</Name>
<Menu>
<Name>Games</Name>
<Directory>kf5-games.directory</Directory>
<Menu>
<Name>Arcade</Name>
<Directory>ubuntustudio-noshow.directory</Directory>
</Menu>
<Menu>
<Name>Board</Name>
<Directory>ubuntustudio-noshow.directory</Directory>
</Menu>
<Menu>
<Name>Card</Name>
<Directory>ubuntustudio-noshow.directory</Directory>
</Menu>
<Menu>
<Name>Kidsgames</Name>
<Directory>ubuntustudio-noshow.directory</Directory>
</Menu>
<Menu>
<Name>TacticStrategy</Name>
<Directory>ubuntustudio-noshow.directory</Directory>
</Menu>
<Menu>
<Name>Logic</Name>
<Directory>ubuntustudio-noshow.directory</Directory>
</Menu>
<Include>
<Category>Game</Category>
</Include>
</Menu>
</Menu>
Place this file in /etc/xdg/menus/applications-merged/
for systemwide configuration or
in ~/.config/menus/applications-merged/
(you may need create this folder) for per-user configuration.
Nothing else to do, it will take a moment for the xdg-subsystem to update and then you will see the changes in the application menu.
I tested this with Ubuntustudio 20.10, 21.04 and 21.10.
This will definitely not work on earlier versions of Ubuntustudio since they come with the XFCE-desktop.