Even then, going from these messy biological details (e.g. these 20 proteins assemble into a particular form and release this neurotransmitter from this synapse when X happens) to an explanation for how the neuron works at a more algorithmic level is hard, and the field isn't there yet. Assembling and abstracting the details is hard and it's one of the goals of theoretical neuroscience. The complexity is probably a symptom of our lack of understanding, rather than the cause of it, i.e. there probably are a lot of details that we can abstract away in a simpler functional model.
I haven't read the paper, and I'm only vaguely familiar with Hawkins et al.'s HTM work. But I disagree with the claim at the end of the TR piece that these predictions are imminently testable. Thinking up a specific experiment to try and disprove theoretical ideas is often the hardest part of experimental neuroscience.
The computational properties of neurons are massively complex, e.g. local filtering in the dendrites, attenuation of depolarizations down the dendrite, the effect of local excitatory and inhibitory inputs, just to name a few. The authors of the manuscript present their interpretation of some of the these properties to achieve the goal of spatio-temporal pattern recognition by neurons (I haven't read past the manuscript yet). Others have done the same.