Fractals have a property called self-similarity, where "a self-similar object is exactly or approximately similar to a part of itself."

John is saying that Apple's products have an "Apple-ness", as does each app on each product, each feature within each app, etc.

He is suggesting that the zen-like simplicity of Apple can be found at many different levels of the organization. I don't think it's overly biased dribble... it's an eloquent point that Apple Inc. is a culture (cult?) with a clearly identifiable philosophy that permeates every element of the org.