If we were to simplify The Kite Runner beyond all reason and good sense, we would say this: the book follows Amir from birth to middle age. Or, we would say: this is a really long coming-of-age story. You might respond: Don't most coming-of-age stories end in early adulthood, when most characters (and real people) mature? That's the thing with Amir: not only does he have to grow up like normal people, he also has to atone for the sins he and his father committed. It's only then that he can really grow up.
In some ways, the scene in the alleyway defines the whole novel. It colors Amir's childhood and adulthood. Amir spends the whole novel dealing with this single, traumatic event. (Like in real life, trauma in The Kite Runner stops time and freezes normal development – thus Amir tries to escape his adolescence for the entire novel.) Really, The Kite Runner is a derailed, delayed coming-of-age story. Our protagonist extends his painful adolescence through guilt and silence until, oh, he reaches the age of forty.
Also, there are two very interconnected storylines in The Kite Runner. We have both the family life of Amir and the life of Afghanistan as a nation. These intersect all the time. For example, right before Amir abandons and betrays his half-brother, the Soviets invade Afghanistan, pitting neighbor against neighbor. We might say the family drama stays in the foreground (what's right in front of you) and the war and national drama mostly stay in the background. Amir's relationships with Hassan and Baba are of central importance. But right beside those relationships – really, surrounding them – are the years of conflict and strife Afghanistan endures. To save Hassan's son and redeem himself, Amir must square off against the Taliban. Soon after Amir "invades" Afghanistan to save Sohrab, the US invades a Taliban-controlled Afghanistan. These two storylines are like peanut butter and jelly, Romeo and Juliet, salt and pepper...well, you get the idea.