I got your point, this is a Articles - Categories module which displays a list of categories, when you click a category title, it will, of course, link to the menu item page of that category.
What you're trying to achieve is kind of using tab, then click a title, it will show a list of articles of associated category. I recommend to use another module for tab to achieve that as this module doesn't support that kind of layout and you have to customize much to have that layout.
