In the short term, yes. In the longer term competition and companies/people entering/leaving the market moves demand and supply closer to something that justified by costs of production and 'value' of product.

(Economists say demand and supply are elastic, I think.)

I agree. Labor is just another input that a company requires in order to create its product. I would expect labor prices to be driven by similar if not the same market forces as goods. Excluding government interventions of course.

Labor theory of value claims that the value of X depends only on the amount of labor required to produce X. This theory doesn't explain how gold is more valuable than iron, or how $UNICORN is more valuable then this other startup. So it's a bad theory.

matthewowen's argument is not assuming the labor theory of value is true. It's just pointing out that, other things being equal, if the demand for X increases then the demand for X-makers' labor increases too; hence X-makers' wages increase.

Which is bullshit, all the way around :)

And what drives demand for labor?