Calling Things Fall Apart a "story" is a fitting characterization because it is told in the style of a third person narrator with little dialogue, giving it a story-telling feel. The third person narrator also tends to use the past tense which gives the tale a historical feel. Being third person and past tense, and with sparse dialogue, the novel can read like an oral tale that has been passed on through generations. Given that it is a tragedy, it also seems like a cautionary tale or fact-based fable.
Note the way the narrator utilizes this oral, story-telling style. As the story of Okonkwo and the Ibo are told, the narrator includes historical and cultural information about the tribe's customs, giving it the style of a story and a history of the culture.
The Oracle was called Agbala, and people came from far and near to consult it. They came when misfortune dogged their steps or when they had a dispute with their neighbors. They came to discover what the future held for them or to consult the spirits of their departed fathers.
That the narrative style has elements of the Ibo culture is significant because the loss/transformation of that culture is one of the main issues of the novel.