You run until the ball stops drifting left or right (bearing) then you work on distance (range). Not rocket science. the range problem is harder than the bearing problem.
I think it works in phases programed in the mind...To really get the answer play frisbee with a frisbee catching dog some day. I’d swear you’d think that he’s zeroing in by smell.
You first run in the general vicinity as the trajectory dictates, then adjust as you get closer taken into account the memory of drift that occurs when eg a right batter hit the ball to right field off of a left hand pitcher.
Over time it becomes second nature.
You see it in little league. Some kids have natural ability to hone in on flies, some don’t as much.