Why do the example rules give fractional dimensions instead of 3?

Because dimension here is measured, not assumed: you count how the number of nodes within r hops grows, and call the exponent d the effective dimension. The specific rules Wolfram studied happen to settle near values like 2 or 2.7, and nothing forces d to be a whole number, so genuinely fractional answers are legitimate. The model's claim is only that some rule could in principle yield the 3 we observe — it does not identify which rule does, and the example rules are illustrations, not candidates for our universe.