My guess would be you start with the out side panel then using a smaller block to seperate the next panel. Then that panel is screwed and glued on the smaller block and so on and so on. Then I would leave the center 5 or so panels to be screwed from the bottom. It looks like to me the panel on the floor is just half laped by the vertical panels, you could screw the panels from the bottom too to make it extra strong. No need for a router you can do it all on a table saw.
If you want I can draw it up for you on cad and send it as a PDF. It wouldn't be hard at all to draw, furniture design is what I do for a living.