A chair used at a desk is dragged - pulled in, pushed back, twenty times a day - and that is a completely different structural problem from a chair that is sat in and left.
Dragging puts a sideways force through the legs at floor level, which racks the frame: the rectangle in plan slowly becomes a parallelogram, and every joint loosens. It is why so many old desk chairs wobble while old drawing-room chairs do not.
So this chair is braced low. A stretcher runs between the back legs and each side, down near the floor where the racking force actually acts, rather than being placed high for appearance. The lion supports at the front are also carried right down to the floor and jointed into a shaped foot rail, which triangulates the front of the chair.
Both are things you barely notice on the finished piece, and both are the reason a chair like this can be pulled up to a desk daily for fifty years and still sit square on the floor.