That does not seem like a lot of play to me- should not cause any problems, but given that it just appeared I understand it can be concerning. I bet the steering linkage was pulled tighter when it was bolted to the input shaft of the steering rack or some other intermediate joint at the factory- that linkage might have been taken apart and bolted back up with a little more slack in it. If it REALLY frustrates you, you can get under there and see if you can check all the connections and re-bolt it with the slack taken out. If it were mine I would probably just live with it.

It should be be that loose. Inspect the u joint and load a longer version of the second video as it’s too short to really see anything.