The synopsis of the video is that the mother rewards the doughnut as a sweet treat for the hard work in school, but refuses to give her other daughter a sweet reward. The video mainly focuses on the problem of fat-shaming and body image, but I see other problems in this video.
First of all, the thin girl is taught to believe that just because she is thin, she deserves praise and affection from everybody she meets, regardless of her actual grades or accomplishments.
Second, the mother's unfair treatment of the girls will teach the thin girl that it's okay to shame people because of their weight or size. In reality, body weight and size are not easy to change. The whole family should work together to eat healthy, so that everyone - fat or thin - won't die of metabolic syndrome.
Third, the thin girl is at risk of metabolic syndrome. Obesity doesn't kill; metabolic syndrome does. Therefore, the thin girl can eat all the shitty food she wants, become "skinny fat", and die by metabolic diseases that are not diagnosed or treated seriously beforehand because the people around her always assume that she is "healthy" simply because she looks thin and pretty.
Fourth, the fat girl learns that healthy food is punishment and that unhealthy food is reward. This is not a healthy association. If she grows up with this association her whole life, she will use unhealthy food (reward) to deal with emotional pain, thereby making her fat problem even worse. Her thin sister will also be a victim of their mother's unfair treatment. The thin girl will also learn that healthy food is punishment and unhealthy food is reward. Even though she may not get fat, she will succumb to metabolic diseases down the road. So, the mother is really harming both girls.
In any case, this video is one dumb social experiment. I know this is all fictional, so no one is harmed in the process. But it's still a dumb social experiment, because no parent would ever do this to his/her child! If a parent does do this, then this is just child abuse. Every child deserves to be loved unconditionally. If the child is sickened by the flu or some kind of metabolic disease, then that child must be treated with love. The whole family should help each other move toward a healthy lifestyle.