screws and glue are ok for butting two pieces together on faces, but screwing into the end grain of such a soft wood like pt pine, or cedar, a bit of side pressure and those screws will crack out of 5/4 or 3/4 decking. I know because after I made a rocker similar to that years ago, the rocker cracked off because I had it attached only with a bit of glue and screws into the end grain of the bottom of the leg.
they are nice chairs on that deck.
the rocker that I made for outdoors use, the one the wood magazine highlighted, used tenons, and I put a screw through the tenon. Its held up nicely.