One of the key points of this theory is that its learning rule is hebbian. A variation of "If it fires together it wires together." Individual synapses make or break connections based on if the input neuron firing immediately proceeds the firing of the next neuron in the chain.

This is distinctly different than say a recurrent neural network where all neurons have outputs at each timestep and weights are updated based on the derived contribution of each weight to the quality of a final output.

The first rule is very local, both in time and space, and the second is in some senses "global."

Backprop has obviously had much more success in ML than any Hebbian learning rule. However we're pretty sure biological learning is essentially Hebbian. The merger / reconciliation of both these rules is one of the most interesting areas of research right now.