Input shaft (worm gear) play

What you see, I presume is with the box not connected to the steering column? This is not play in the worm gear. Install the column and make sure that the output shaft in the steering box is turned so that it is all the way in and then make sure that the column is installed so that it is fully seated onto the shaft and tighten it in place. Then see what your play is at the steering wheel and adjust at the box as needed.