It's weird they'd say "classical economics" - the Baumol article links indeed to classical economics/classical political economy but the linked article doesn't bear out the claim. The actual situation is that the original field known as "classical political economy" made the claim that wages are indeed a matter of the cost of reproducing laborers whereas a "modern economics" or "neoclassical economics" as a field/label is where the claim that real wages are tied to labor productivity changes appeared. The particular wages-productivity theory seems to have been articulated around the 1930s [2].

[1] https://en.wikipedia.org/wiki/Classical_economics

[2] https://en.wikipedia.org/wiki/Marginal_revenue_productivity_...