Worm gear preload is the first step when rebuilding an old ford steering box. If done proper, that setting will not change for many thousands of miles. Next step is set the depth of tooth contact between the worm gear and the sector shaft. That setting can wear over many thousands of miles, thats the screw you found.
I'm guilty in this area, I seem to set them up on the loose side, feels good on the bench, then once in the car with real world happenings, its got some play at the steering wheel.
I don't care, but if you do want to take that play out, keep in mind the worm gear is not a straight cut gear, its high in the middle. Reason is, the middle is going down the road straight, probably 98% of the time, so that area is machined bigger to allow for wear.
If you tighten up that adjusting screw, it must be done at dead center of travel, then crank the steering lock to lock and see if it binds up at the ends. if so, the worm is worn beyond adjustment. if the travel is smooth, live with the play at the wheel if its not outrageous