The play , under control of the spring, is there so the stand can move slightly around any small obstructions on the ground, gravel etc, when being put up or down. Thus preventing strain on the stand mount and frame. It makes it easier to use.
Mine (2016) does exactly the same as your video, always has, and has never changed. I did take it apart using the " pennies between each spring coil" trick when I first had it, to replace a shortened sidestand that went with an unwanted lowering kit.
My opinion is that mine is fine, and acts like it was designed to. I just checked my other honda ( pan european ) and it does exactly the same.
I would not modify the stand in any way. Mr. Honda knows what he is doing in my humble opinion.