The astronomy knowledge and the mechanical theory needed to make the Antikythera mechanism were well known in ancient times, and I don't think those were ever lost. The mystery of the Antikythera mechanism is how it was actually built.
But do we know how long it took to build?
If it was built in a short time frame, then yeah, the maker probably used techniques that were lost not too long afterward, and not rediscovered until maybe the 14th century.
But what if it were built over a much longer time frame? It could have been someone's lifetime project. Then simple techniques might work. For instance, if you need a piece of metal shaped to very tight tolerances, just get it close and then use a hand file to very slowly make it what you need.
If this were the case, I can easily imagine that plenty of people between the time it was made and the 14th century knew how to build one, but simply were not interested enough to make building it their life's work.
The author is more of a physicist than a historian, fwiw.
(Then I read the news and cry in my corn flakes, of course.)
Due to the laws of thermodynamics I have little belief left for a beneficent (let alone malignant) secret society of any stripe. But I could be wrong. There are more things in heaven and earth and all that.
It's more a poetic application of statistical mechanics than a rigorous one.
And their gods too?