You are right. It is a type of blackmail, indirect blackmail. Blackmail is produced by the use of a situation, not by the power relationship the blackmailer has with the blackmailed. If we dispense with Zach as a handsome boy and younger than the teacher, who theoretically has a situation of power, and look at the characters and their interrelationship blackmail is very clear. It happens in the business and artistic world.Zack blackmails Sophia! Manipulation of his behavior in front of director Briks. This is exactly what blackmail is!
Yes, this is not "hard" blackmail, but it fits well into story - student life.
For example, a film production needs a certain middle-aged actor (he is not going to be handsome) and the director of the casting agency, who has a lot of money at stake and the prestige of the agency, sends a beautiful and very effective assistant, with a promising career, to get the actor to participate in the production. The actor tells her he will think about it and if she wants to go out to dinner, she declines the invitation. The assistant comes back and the boss tells her that the actor is needed, to do what she has to do, that the agency's business and her own promotion (or that of her boyfriend, husband, father...) depend on it. Of course, the actor knows or suspects that he is needed and that the consequences of not participating in the production will fall on the assistant, and the director of the agency suspects what the actor is asking for, or simply does not suspect it and does not care, he just wants results. This is blackmail. NTR idea.
In this story the main element of blackmail is the director, who pressures the teachers so that Zach does not stop playing. But the evolution of the pressure is peculiar, one of the successes of this story because of the paradox it raises. The story begins because the couple of teachers do not want to give a pass to the basketball player because they consider it unethical. But the story takes a turn that leads to Sophie's behavior that could be anything but ethical. The principal goes from demanding a passing grade for the two, to demanding that Sophie do whatever it takes to get Zach to play, and that if she doesn't get it Felix's promotion won't happen. Moreover, the director more than likely knows what Zach wants and is getting, and Zach knows what the director's reaction is and who he is attacking when he doesn't play. This is blackmail.