The approach of the paper is to use a genotype/phenotype distance correlation plot to study the complexity of a system that is determined by a genotype and exhibits som ephenotypic behavior. This is equivalent to simply plotting the distance of two phenotypes (Hamming of the state after 100 iteration starting from a single activated cell for CAs) against the distance between two genotypes (Hamming distance between the rules for a CA).
The approach is interesting, and I also believe that a sensitivity analysis of the behavior of a CA w.r.t perturbations in its rule is worth looking at. However the distance correlation plot itself is very hard to interpret and read, which is probably the main drawback of the method. There is no clear interpretability.