What happens if you tighten the bolt? Sure looks like a clamp of some sort, maybe with a cam involved?
Gotta be a simple answer out there somewhere.
(My simple answer involves drilling holes for anchor screws or a through-bolt, just because our tables get whacked and shoved frequently and an adjustable mechanism finds that hard to deal with. Mostly, "adjustable" is just for turning the banquette into a double berth)
I think Christian is right, try to gently tighten to see if it has a effect. That assembly is there for a reason, likely hiding a cone nut or cam. Maybe an off the shelf shim or washer will compensate for wear, perhaps it is the table post that is deformed. My post is deformed, as well as the base and top clamps, so it wiggles a little(my model is like Christian's 381 beige one) . If you can't get factory support from Zwaardvis, or other source, take pictures as you disassemble it, so you don't have to guess multiple times how it goes back together, a lesson I often relearn from time to time.
Mine still has the overly-engineered OEM table knob. It is identical in shape to the pedestal post height adjustment knob. As you tighten the knob (clockwise), it pushes another over-engineered metal level plate inward against the post preventing the table from rotating. It does not work terribly well unless really cranks down on the knob. I will take a picture next trip.
You probably noticed the table is off center with respect to the pedestal post. Rotate one way to reduce amount sticking out into the walkway, rotate another way to accommodate settee sitting room.
Yalcin, here are couple pictures of the Zwaardvis table knob, not sure if it is identical design as yours. By tighten the knob, the finger shaped piece slides down the slope and pressing against table post. Like I said, over-engineered.