Looking at the three washers you have at the bottom of the vertical steering shaft gear in the video they may be keeping the shaft from fully engaging with the larger gear teeth on the cross shaft. If you only had one washer in there the steering shaft could slide down a little further into the bushing - just an observation. If the shaft and smaller gear are not too hard you could drill a 1/8" hole in them at the top surface and insert a 1/8" split pin so the gear is pinned tight to the shaft. Looking at the video if the hole is up there it would not affect the gear teeth engagement. Just a couple of suggestions if you want to eliminate the play.