That’s going to be a lot of work, because the class that is used to generate these tables contains some private functions for building the html. This means you cannot call them from within the callback function that you specifiy when you add the submenu page for the list of posts in a certain category (the use case you explained in your previous question).
So you would have to clone that code and pray everything ends up fine. Things would be a lot easier if that automatically generated was a custom post type…
Anyway, if you’re stuck with everything in the standard post, there might be another way to declutter the posts overview. As you can see on the line with “bulk actions” you can select categories. Unfortunately you can restrict to a single category, but not exclude one.
However. This dropdown list is generated by wp_dropdown_categories. By the end of that function you see a filter that lets you manipulate the dropdown list. You could use this to add a line <option class="level-0" value="-7">Exlude Events</option> to the dropdown. If you select that line you should get everything except category 7.
Disclaimer: I didn’t try this out, it’s an educated guess.