This is a very nice table and certainly worth a restoration. I'm guessing the legs were originally joined by mortise and Tenon. When the joints got loose, the previous owner installed the screws. A very bad decision but one you might correct by re-gluing the joints after you've stripped the old finish and doweling through the joints to lock the joints and to fill the holes made by the screws. Good luck to you.
If you don't have time to do it right the first time, when will you have time to do it over?