5/4 Oak, frame and panel. Fumed finish, with a wiping varnish.
Main table section is two rails and four stiles, T&G, tongue and grooved. ( It could also be interpreted as 4 rails and two stiles. ) The wings are a 5 piece T&G, framed panel.
From a design aspect, it's very important that the size of the rails and stiles are "present", or thicker than 3/4". (4/4.)
One other subtle design element is that the ends are M&T joint, to hide the T&G grooves.
The panels can be any thickness, up to 5/4, but you're better off staying with 5/4 for mass and strength. Th eT&G has to be adjusted to bring all of the surfaces into the same plane. I would use " Space Balls" to hold the panels and only glue them in the very center of the panel, if at all, so that the panels can float.
It's simple piece, but the devil is in the execution of all the joints to pull square.
It can be done with a table saw, using stopped dados, but a router, and benchtop Mortiser would make things easier. A lot depends on how period specific you want to be for construction.
You want the Benchtop Mortiser for the base anyway, and if your desire is to replicate the Mission/Craftsman styling, you want a benchtop mortiser with a tilting head. I promise. 1:6 is a common mission angle for through tenons.
I've taken quite a bit of Stickley furniture apart through the years and repaired them. I'm fairly certain of the construction of that piece if was period authentic.
It looks like a David Rago/ Jerry Mortimer auction piece. I have one similar downstairs in my basement.