The widget displays in my front-page sidebar only when I am logged in, and disappears as soon as I log out. All public users / anyone else viewing the site would not see the My Link Order widget.
This is independent of the category/categories used, link order, etc.
I have only seen this behavior with this widget.
website: http://www.nowlikephotographs.com, the My Link Order widget should appear at the top of the right sidebar.