First video: Low booster vs HBB. This is pretty convincing IMO about the need for the extra protection, it's not even the side wings particularly (in this type of crash) but that little clip holding the seatbelt close onto the child's shoulder with a high backed booster. Ignore arms flailing about, what you're looking for in crash tests is movement of the main part of the body (shoulders to hips) - less is better - movement of the neck, any sharp movement will cause injury, and anything where you can see the dummy "folding" over a seatbelt or strap or the straps/seatbelt cutting into any part of the body is very bad as this shows what would on a human cause internal injury. Try to imagine also the distance of the other seats, car doors etc - if the dummy is moving from the normal seat area into an area where these things would be present, that's a blunt force trauma injury too, that can kill instantly if it happens to the head.
Then the second video shows what looks like two fairly large child dummies (judging by the height, 7y and 10y? Hard to tell.) and what happens without a booster - this is called submarining.
Third is clearly labelled, 10 year old dummy. Clear submarine and that neck movement looks brutal.