Marxism preaches the removal of all class systems, with only a neutral government to oversee collective labor. In The Kite Runner, the various class systems are a integral part of the Afghanistan culture, leading back thousands of years. Since their culture is overpowered by Russia, and so their own class system becomes subordinate, they can't be said to have Marxist leanings; besides, their class structure came about years before Marxism. However, the Russians of the time show Marxist tendencies, especially when they use their authority to abuse the Afghan people.
I think it isn't necessarily a "marxist" novel. Unless you mean it predicts the uprising of marxism and the start of communism. That could be somewhat truthful. However, the presence of class distinctions is actually captialist. In that cases, the class system and the "unrest" would promote marxism. Yet, there really was no unrest of the lower classes. (As there was in Pre-Soviet Russia). The Afgan culture was such that the Sunni and Shi'a were used to the situation. They didn't appear to fight. The classes that later came to power in Afganistan seek to eliminate the established lower class. To me an arguement can be made that the novel was more fascist. But, anyway, the communists didn't really have everybody "equal". The ones in power had more the the "masses".