My 94’ Jeep cherokee 4.0l 2wd has had an issue that the steering over the course of several years has get some play in it now. It also makes sounds as documented in the video. I should also note it doesn’t seem to do it when it’s warm, but when it gets around 50ºF or lower the problem is there.
Very likely the problem is the steering coupling that is in the steering shaft just above the steering gear. With the key turned to release the steering wheel reach down behind the steering gear and twist the shaft left to right and if it has any free play the coupling is shot. It is available at any McParts store for a few bucks.
I just discovered that these steering boxes are offered everywhere as off the shelf parts. I’m unable to find any technical information on them, however it looks from the ready availability of replacement boxes like that might be a common problem with that box. Or with that rack.