I would totally agree, that "The headmaster" heavily plays with ideas of "Autoritarism". And I admit, that this could be seen very critical. But it lacks something that determines a dystopian story like Orwells "1984" or Kafkas "The Process" in my understanding quite a lot, and that is the characters permanently struggling with the system in which they live and more important: the hopelessness of that struggle. That's neither for the headmaster nor for the students the case (Ruth and Mr. Wilson are maybe the only exceptions
, but they are not in the focus). I thought a little, whether there are lewd games, that fulfill those criterias, and I would put rather games like “Caseys fall” and “Fashion business” in a dystopian lewd games category.
By what the game is now and in the logic of the game, the headmaster is rather a pervert antihero, who "helps" the girls with his punishment-measures to graduate from school and develop their own strengths, and might finally maybe even start a fight against Mycocks System, which he is by now only blurred aware of (as far, as I remember). The students (after some struggle) adapt to the system of the headmaster and even draw advantages from it, what makes the overall tone of the game, despite the dark setting, rather positive.
I personally would define a "happy ending" in the logic, the game represents by now. I would see it as an ending, where you graduate the girls and the later life of the girls going a way you would like for someone you have "trained" (whatever this is (harem, professional success, etc.)). In an exaggerated way, the MC could even get a price for his life-work by the secretary of education, who just does, whatever is popular in the public. Of course everything in the lewd logic of the game. If this would be done in real world, the actions of the headmaster would be totally to condemn.
To have the girls stripped from their rights completely in the end would be hard to make plausible, as you train them even to be more self-confident (and at least for me not enjoying). If they come to your harem, it would be rather on their own will.
I would find the last ending actually also quite funny to watch and thought about if such an ending was possible and plausible to explain, if popularity drops to zero, because then the events of the school might drop to the public. Some weirded-voice in my head tells me, that in this case even Mr. Wilson might overtake the school as the new headmaster, being far more popular then the MC.