Wages are a function of the scarcity of labor. Advances that increase the productivity of workers often also makes it easier to do those jobs, hence a larger labor supply that pushes the price of labor downwards.
This assumes an unconstrained "market" for the exchange of labor and wages, just as the claim that "prices are a function of the scarcity of goods" assumes an unconstrained "market" for the exchanges of goods and money.
But this is not the only model for economic exchanges of labor, goods and money. The Romans, for example, did not use market pricing, but instead were primarily a "cost-plus" economy (you paid the cost plus a known margin).
I know it is extremely hard when most of us have been embedded in a neoliberal, market-centric culture for our entire lives to think this far outside the box, but there really is no law of nature that says that what I pay you to do work for me must depend on how many other people could do the work.
In a culture that viewed the economy as a tool to enhance the living standards and quality for all of its members, there might be a very weak or even non-existent connection between labor availability and wages. Productivity gains could be viewed as way to either (a) reduce the amount of labor required (b) increase the amount of goods & services available, or both. Wages could remain fixed, or increase in such a scenario.
This is nothing like the economic system in which we live, however; an economic system that is viewed as a playground in which which some will accumulate vast resources (and thus power) and others will not can never function the way I just described.
That some theoretical other economy might exist does not belie the one this article discusses correlates wages and scarcity of labor, nor does it preclude anyone from making different decisions about pricing their own labor.