Hi,
I am also surprised why only one chick is left.
I saw another pair with only one chick as well.
I believe I read an article in the German bird watching magazine "Vögel" which described that coots commonly aggressively discourage chicks from begging for food instead of foraging for themselves. So the kind of behaviour you describe in your headline is typical for coots.
(As your Youtube link somehow doesn't make it through my various spam filters, the headline is all I'm going by.)
Coots employ a strategy of breeding for numbers, in a habitat that can be difficult with regard to food. They time their breeding so that the chicks hatch one after, so you can have older chicks in full immature plumage alongside freshly hatched pulli.
The older chicks often also help to feed the younger chicks.
It seems that sometimes, the "feeding" and the "discouraging" instincts collide, and then the parents (or, as my girl friend once observed, older siblings) alternate between feeding a begging chick and attacking it.
I'd say that normally, the chick should be equipped with instincts to either endure the attack (if it's truly unable to find food on its own), as the parents aren't actually out to harm the chick, or to go and find its own food (because the parents would be instictually equipped to only discourage fit chicks from begging).
Of course, there are situations when there just isn't enough food around for all the chicks to survive, and then it can be nasty. However, normally this kind of behaviour seems to be a adaptation that ensures the best chances of survival for the greatest number of chicks.
Regards,
Henning
[Edited to get rid of nonsense apostrophes]