How is this proving anything about broader economics? Or any of Marx’s boondoggle social claims?

This just says that calculating the summation of all labour costs is a good predictor of the overall cost of production and thus price, Marx makes way broader and wilder claims than that.

Defending marxist views on the LTV with this paper might as well be a motte and bailey; there is no substantial dispute that the sum total of costs is a decent predictor of an industrial good’s price (industrial production per-product margins are notoriously slim), while there is plenty of dispute that the generation of “surplus value” causes “alienation” and “dehumanization”.