I think the phrase could be interpreted to mean that the will or spirit of K'n-yan animated the headless body of T'la-yub and was thereby responsible for the seizure of Zamacona. This is a realization that the "Author" comes to in the last lines and shows the futility of trying to do anything against the mound or the beings within as the whole power of the beings is funneled through the living-dead.
In my interpretation it shows that K'n-yan was already aware that Zamacona would attempt to escape and was still able to prevent his escape, as forbidden by the court:
It was now made plain to him, though indirectly, that his own penalty for another escape-attempt would be service as a gate-sentry—but in the form of a dead-alive y’m-bhi slave, and after amphitheatre-treatment even more picturesque than that which T’la-yub was reported to have undergone. It was intimated that he—or parts of him—would be reanimated to guard some inner section of the passage; within sight of others, where his abridged person might serve as a permanent symbol of the rewards of treason
K'n-yan was able to do this even though Zamacona was practicing dematerialization:
What gave him a final hope of scatheless escape from K’n-yan was his growing mastery of the art of dematerialisation. Having studied it for years, and having learned still more from the two instances in which he had been subjected to it, he now felt increasingly able to use it independently and effectively...
...The only trouble would be if he failed to maintain his spectral condition at all times. That was the one ever-present peril, as he had learned from his experiments.
The "Author" of the manuscript goes on to speculate that perhaps something happened to Zamacona, such as the feared re-materialization and that he was captured, perhaps by T'la-yub (emphasis mine):
Zamacona must have barely reached the outer world when overtaken by some disaster—perhaps an involuntary rematerialisation. He would naturally, in that event, have been seized by whichever sentry happened to be on duty at the time—either the discredited freeman, or, as a matter of supreme irony, the very T’la-yub who had planned and aided his first attempt at escape
What the author didn't realize, until he saw the headless etc. body of Zamacona was that they are essentially powered by the supremely powerful will of the beings under the mound and have been preserved in that state more or less indefinitely as a warning to others and a punishment for the individual involved.
Yes—it had been a very human being once; and what is more, it had been white...
...if that manuscript was as true as I think it was, this being had been used for the diversions of the amphitheatre before its life had become wholly extinct and supplanted by automatic impulses controlled from outside
Edited to add: as to how it is moving, it seems perhaps flopping or stumbling on stumps:
Then there was a sound—a flopping; a padding; a dull, advancing sound which heralded beyond question a being as structurally material as the pickaxe and the shovel...
...The padding grew more distinct, and from the mechanical cast of the tread I knew it was a dead thing that stalked in the darkness.