The adjust bolt on the top is for alignment of a runner wheel with a worm screw inside the box. there will be a sweet point at which there is "minimal" play between the worm and the runner wheel. too high and the play will be worse, too low and the play will be worse.
the adjust bolt simply holds the top of the steering shaft in a certain up/down position, but allows it to turn. the adjustment just aligns with the input worm gear.
"minimal" play should be reasonably tight, but will still have a small backlash.
if your steering is quite sloppy, i'd also look at all the adjoining bits, like ball joints, splines and steering u/js, perhaps the bearing at the bottom of the steeing box etc.
for power steering systems, the input worm gear also has a spring loaded "choosing" valve, and the spring might be a bit weak. there is also an adjust for power steering for the tightness of the piston-to-shaft partial gear. this is adjusted on the engine side of the box, very small adjust here to take out some slop.
