I have only ever flown Mini's, started with the Mavic Mini, then Mini 2, a Mini 3 and now also have a Mini 4 Pro. Reason for that is that I do a lot of multi day backpack hiking routes so weight is of paramount importance.
I have found the...
The props on my Mini 4 Pro have the same amount of play.
Have you compared yours? The movement might look more pronounced in the video since it's zoomed in on the action.