I don't know whether that was intentional or not, but it kind-of is.
Each of the game's chapters represents a different sphere of influence or obsession which can, if not navigated correctly, make an individual conceited or trapped. A different subcultural mechanism of defining value and establishing an in-group and an out-group to help form identity.
Together, these form a picture of an arbitrarily divided populace, with Gary being a human manifestation of the desire to divide and define people overall, and with the game's story being about staying individual to combat and dismantle that. Jimmy rejects the idea that the students of Bullworth Academy are actually different, and eventually unites them all against their common enemy - division itself.
Chapter 1 is about the purest form of an in-group possible, which is simply based upon familiarity. The bullies don't really have any enemies, but they do stick together as a group because they know each other. This makes them a very good and self-contained vehicle for an introduction to the game's narrative, and Jimmy beats this group simply through familiarity. He might physically beat Russell in a fight, but Russell doesn't even care about that - he only cares about the idea that Jimmy might have insulted his mom. By the time that Russell finds out that this isn't true, he has grown more familiar with Jimmy and accepts him.
The lesson of Chapter 1 is that division, and forming groups, is an innate part of human behaviour that requires literally nothing else to exist other than pure familiarity between people.
Chapter 2 is where it gets more complex, with the Preps instead basing their in-group on another factor that can define and trap people - materialism. They define themselves through opulence and fashion, and view themselves as better than others because they have access to it. Jimmy beats this group by becoming their boxing champion regardless of his lack of opulence, showing their obsession with it to be meaningless and functionless junk. He is societally disadvantaged in their view, and still wins. In doing so, Jimmy does actually gain some wealth by winning the beach house and, essentially, controlling the boxing gym, and wins the appreciation of most of the Preps.
The lesson of Chapter 2 is that materialism is a form of arbitrary division that doesn't represent someone's actual value, and that becoming obsessed with it will leave you lacking any actual substance.
Chapter 3 is the antithesis of Chapter 2. Instead of being obsessed with material possession, it's about being obsessed with emotional possession. Johhny has constructed a cult-of-personality around himself, but is himself infatuated with Lola and can't view himself as respectable or valuable without her. They view themselves as being entirely different to the rich Preps, but they're focus on fashion and competitive sport (bike races) is just just the same as them. Only, the Greasers define themselves as being the romantic underdogs. Johnny is obsessed with maintaining his image (just as the Preps are), but his need to emotionally possess Lola leaves him stuck. Jimmy defeats the Greasers not by beating Johnny himself, but by beating Lola. By the end of the chapter, Jimmy has tired of her and recognises her as a negative influence upon everybody. Jimmy's ability to value himself beyond women is what, ultimately, impresses Johnny.
The lesson of Chapter 3 is that romantic obsession does make the world go around - but it can also make your world stop or leave you shallow.
Chapter 4 is essentially two chapters, but in one. The Nerds define themselves through academic intelligence and value people primarily through that lens, whereas the Jocks define themselves through physiological prowess and value people through that lens. Importantly, both are examples of anatomical skill - one group trains their nervous system, while the other train their musculoskeletal system. They define themselves as opposites and don't realise that, ultimately, they're two sides of the same coin. They both play games, but one is focussed on mental roleplay (Grottos and Gremlins), while the other is focussed on kinetic movement. Jimmy beats the Nerds by showing that you can't rely on intelligence to beat raw power (defeating their engineered defences), and then beats the Jocks by showing that you can't rely on raw power to beat intelligence (sabotaging the game with an elaborate plan).
The lesson of Chapter 4 is that a balance of intelligence and strength is better than becoming conceitedly one-sided.
Chapter 5 is about the anti-establishment itself, and defining yourself purely through the lens of being an opposition to order. Basically, anarchy. The Townies define themselves through being a disruption to the established order of Bullworth and Bullworth Academy, and view themselves as better because of it. Jimmy beats the Townies not by beating Edgar, but by exposing Edgar's hatred of Bullworth to be meaningless and, ultimately, something that only serves someone else's designs upon control (Gary). Jimmy beats the anti-establishment not through force, but through evidencing the value of the establishment as a defence against even worse things.
The game's narrative is fundamentally about how everyone is the same, albeit expressed differently and constantly being affected by the same innate drive to form in-groups and out-groups. Jimmy defeats these groups, and returns the school to a better state of unity, by defeating the aspects that they use to try and differentiate themselves from others. He surpasses unfimilairity with the Bullies, material possession with the Preps, hopeless romanticism with the Greasers, stupidity with the Nerds, strength with the Jocks, and aimless destruction with the Townies.
The game can even be sorted into 3 repeating plot conflicts:
Establishment Dysfunction Vs Anti-establishment Dysfunction (Bullies Vs Townies). The Bullies are dysfunctional, but in a way that is accepted by the establishment. Their behaviour is seen as a normal part of the established order, and they are still a part of it (still Bullworth students). The Townies are dysfunctional, but in a way that challenges the established order and is seen as abnormal - something to be stopped.
Materialism Vs Human Connection (Preps Vs Greasers). Told through a rich Vs poor dichotomy. They view themselves as entirely different, but they both are heavily focussed on fashion and on a compeitive sport (boxing Vs bike racing). One defines themselves as the elite, while the other defines themselves as the underdog. One is obsessed with the material and connotations of class, while the other is obsessed with romanticism.
Mental Capacity Vs Kinetic Capacity (Nerds Vs Jocks). They view themselves as entirely different, when they are actually different expressions of anatomical skills. They both have games that they love, but are stuck in viewing the other as their enemy.
The fundamental lesson of the game, I guess, is that balance is important. Don't define yourself so rigourously through a single metric, or you might end up like Johnny or Edgar. And, one day, maybe you'll encounter your very own Jimmy.
And he only gives people what they have coming to them...
