Will a 6x6x16 pressure treated lumber be okay for a play structure with a single super swing
A swing frame  must be very rigid or the energy put into the swing gets sapped, causing it to quickly lose momentum. This is why you rarely see swings on posts. I'd stick with a proven design, the A frame. If you really must use vertical posts, go at least 3 feet down. With 10 feet above ground the torque will be quite strong. 

Interior diagonal braces effectively reduce your beam span. You could easily cut 3 feet from each side, leaving 10. I'd trust a select 6x6 to span that just fine. The braces must be securely fastened, though. I'd consider mortising them into the beam and posts.