First, I wonder how you got access to the article? It is behind a paywall and not yet uploaded to the sites I usually find paywalled articles on.

Second, there is no need to compare brains to neural networks because brains are neural networks. Neurons form vertices and axons edges connecting the aforementioned. What you are perhaps thinking of are artificial neural networks - most of which are very dissimilar to brains. But even then you are wrong. Artificial Izhikevich and Hodgkin-Huxley neural networks attempts to closely mimic the behavior of real neurons.

While deep, hierarchical artificial neural networks have been more successful than biologically plausible ones, that may be because the technology isn't ready yet. After all, the perceptron was invented in the 1950's but didn't become prominent until the 2010's (or so). Perhaps we need new memories that better map to (real) neural network topologies, or perhaps 3d chips that can pack transistors in the same way brains pack neurons.