Not normal.
If the screen "shakes" due to vibrations or other movements my first thought is a loose connection inside the laptop.
Try to do some testing that correlates laptop movement or vibrations with the screen shakes.
Then contact the seller and report the problem.
I might have been unclear, it's not the displayimage shaking its the "chassi" making it look like the display is shaking, its very thin. I tried replicating this on a sturdier surface and it did not replicate the problem if it had I would've bought the loose connection.
Tried replicating this on my phones display too, same stuff. So I guess it's the table being weak. Moving up and down quickly as the tabletop is very thin. Just moving the laptop around does not do this.
So onward to the question; would this be able to damage the screen itself?
Also holding the screen, giving it support does lessen the impact of the "shakes". So do you think theres anything to worry about?