I call this a semi-recessed square leg. Even though the legs technically project from the panel, it creates the illusion of them being semi-recessed into the panel like a pilaster column in a wall. There's a panel connecting the two legs at each end, and this panel is slightly recessed from the legs in order to give the legs a three-dimensional look. If you set you panel flush, it defeats the purpose of having legs.
These legs are wide enough to simulate the door style, and they also have a bit of molding at the top and a base trim that projects a bit from the face of the leg. The stone countertop has been designed to follow the projection of the leg, and has a profiled edge, adding another level of detail that makes this island feel like a special furniture piece.
Tip: There's no rule to how much you should recess the panel, but I typically do 1/4" to and 1" max.