Do you have a link to that article, if it's online? It sounds like an interesting argument (although I'm not sure building a huge tomb for a hereditary monarch is an argument for central planning!)

It would be good to see that article to parse out how exactly the author is analyzing the Egyptian economy of the Old Kingdom, especially because Egyptologists don't always use the same terms and definitions as Economists. Still, there is considerable overlap in concepts. For the most part, the economy of the Old Kingdom is considered an example of central planning, but it isn't described in exactly that way. I'll cite a short passage from The Oxford History of Ancient Egypt from the section "Old Kingdom Economy and Administration" to illustrate:

The state’s main contribution was organizational, including such acts as the prevention of local famines by bringing in surplus resources from elsewhere, the lessening of the effects of major calamities (such as low inundations), the elimination of damaging local conflicts by providing arbitration, and the improvement of security.

That entire chapter provides a great deal of insight into the consensus view among Egyptologists on the organization of the economy during the Old Kingdom. It is generally accepted that the task of constructing monumental tombs required a great deal of central planning, for obvious reasons. The workers who built the pyramids were corvée laborers, conscripted from the general population to work in exchange for grain from the royal granaries. Their work took place during the annual flood, when their fields were underwater, so they were able to earn extra income that would not be available to them at the time from trade or subsistence agriculture. Of course, the grain used to pay them was taken in the form of taxes, but a generous portion of that came from large estates, so there was a sort of wealth redistribution happening as a component of this project. That fact, coupled with the deliberate choice to only employ workers when they had no other means of earning money, suggests deliberate economic planning from the top down.

Edit: I forgot to address the "without markets" part of your question. Again, I would need to see the article to know what is meant by that exactly, but on the surface it rings false. The market system that existed at the time of the pyramids had been in place for millennia already, and it probably operated largely outside of direct state control even during the Old Kingdom. Our best evidence for the Egyptian market economy comes from much later periods, where preserved legal documents provide textual evidence, but there is no reason a priori to posit a different economic system earlier, and it strains credulity to try.