Conversational
You could say that the narrator's story is a kind of rehearsal. Emily's teacher (or counselor) has asked her about her daughter, and over the course of the story the narrator is thinking through her reply.
We bet you've done this tons of times before. You're about to have a difficult conversation with someone – your mom, your boss, your crush – and you practice the conversation in your head.
That's exactly what's going on here. This story is a kind of one-sided conversation.