It's probably not a science, using a falsifiability criterion for "science". (See Popper.) I don't think that's controversial -- Marxist informed hypotheses could be tested and discarded perhaps, not Marxism itself.

Because it's more than that. It's a explanatory model, it's a body of knowledge, with core normative concerns and areas of study. It is, god forbid, a practice; it isn't a disembodied law which regulates the world unarticulated, but which has been apprehended at a particular historical moment, and which motivates and creates a World precisely because it has been apprehended and articulated. (I would conceive of this as it's dialectical character.)

It's not poorer for this; its just a different kind of thing.

I'd be curious to read anyone's opinions on a traditional, Hegelian inflected Marxism with "analytic Marxism" (I've not read Cohen; I wonder if he tries to "ground" Marxism in more "common sensical" empiricism, and whether this makes it more similar to falsifiable science).