Holy cow, I wrote a book!
This is one of those poorly-worded options.
In the Start menu configuration dialog, you can choose to uncheck
"Enable dragging and dropping".
This setting disables drag/drop but also disables right-click context menus.
The connection between the two is explained in the Group Policy Editor,
but is unfortunately oversimplified in the general-public configuration
Why does disabling dragging and dropping also disable context menus?
History, of course.
Originally, the "Disable drag/drop on the Start menu" setting was
a system policy, intended to be set by corporate IT departments to
prevent their employees from damaging the Start menu.
With this setting, users could no longer drag items around to rearrange
or reorganize their Start menu items.
This is a good thing in corporate environments because it
reduces support calls.
But very quickly, the IT departments found a loophole in this policy:
You could right-click an item on the Start menu
and select Cut, Copy, Paste, Delete, or Sort by Name,
thereby giving you access to the operations that the policy was
trying to block.
Therefore, they requested that the scope of the policy be expanded
so that it also disabled the context menu.
In Windows XP, it was decided to expose
what used to be an advanced deployment setting
to the primary UI,
and so it was.
Since it's the same setting, it carried the loophole-closure with it.