It really depends on what you mean by "primary contribution"...
Look: Marx started his adult life with an adolescent oppositional stance, an Enlightenment confidence that he was living in the age of humanity's liberation, and a big chip on his shoulder as a German Jew when all the real action seemed to be going on in the west in France (politics) and in Britain (industry).
So he started out thinking he was going to change the world and liberate humanity by thinking clearly: built on top of material plenty created by British industrialists and the politically-aware people created by French revolutionaries, German philosophers could think clearly, and as if it were scales would fall from people's eyes and they would see: free from their illusions and their prejudices and their misconceptions they would build utopia. So he writes books with titles like The Critique of Critical Criticism and begins what will become a lifetime flirtation with the rhetorical mode of The Revelation of St. John the Divine.
Then he noted that nobody really cared about philosophy, especially not the Prussian secret police. And so he transformed himself from a German philosopher to a French-style political activist as his principal focus, and worked to create the political-revolutionary people necessary for the philosophy to do any good.
Then came the crash of the revolution of 1848, from which Marx drew the lesson that political revolution could not succeed unless and until society was ripe, and that ripeness was a result of slow processes of technological, social, and economic change. And so he transformed himself again into a British-style economist tracking and analyzing the development of the market economy as his principal focus. Unfortunately, he was not a very good British-style classical economist--a "third-rate post-Ricardian" as a technical economist, as Paul Samuelson said to be mean. He vanished into the swamps of the labor theory of value, and never came out.
So what is left of Marx's project?
- An undeveloped philosophy of human liberation.
- An oppositional, revolutionary political stance (with absolutely no sense of how revolutions eat their own children).
- About ten paragraphs' worth of asides in the "Communist Manifesto" and in the preface to "A Contribution to the Critique of Political Economy" about how economic change creates and transforms social classes which then struggle for political power and how those struggles then shift the path of economic development."
The third of these is what I would claim in is Marx's "primary contribution"--and for anthropologists and historians it surely is. But it is really only ten paragraphs laying out this theory of "historical materialism." It's a powerful insight--but it is not a huge part of his lifetime work. I wish it had been: the historical materialist chapters of Capital in which he tries to apply his ten paragraphs are very good.
But outside of history and anthropology the Marxists I meet are overwhelmingly, and increasingly (1) and (2)--plus the (fortunately fewer and fewer) stooges in search of a Stalin.