Matrix is a cultural commentary and an appeal to individual free will. I don't think the actual universe or action in the movie is that important, it's more visual candy.
If one imagines life as a constant grind for money, family and other basic elements, this is essentially what is portrayed as the system, or the matrix. It is predictable, deterministic even. A person's entire future can be predicted, planned, calculated like an equation. And the rebels in the matrix rage against being deterministic.
Neo as a character is not an average guy. He is a highly developed soul, but presented in a relatable way. He is not representing the masses, because it takes a certain level of personal growth to arrive at the stage where the system becomes noticable. Most people never reach that stage and are instead unconsciously integrated into the society, rather than breaking away from it.
The main character, who notices that they are a cog in the machine, starts asking questions, making their own choices and they realize how it involves going against the whole system or needing to escape it. Over the course of the story he joins a rebellion, realizes that all out conflict against the man made world and reality leads to the destruction of the whole world, or their death, and finally learns how to balance his individual needs with common good.
It's a lot like positive disintegration or mental maturity post physical maturity, realizing one's own individuality. The authors, considering who they are and what influenced them must have been going through a process of positive disintegration and becoming aware of that before they wrote it down as the movie.
It's kind of a revolutionary movie in the sense that Neo is the template of a revolutionary character who everyone can feel inspired to follow, but not everyone can follow. Because the revolutionary idea is questioning reality, society and the whole materialistic world and most people are not equipped to attempt that.