When Fisher etc. say we must return a focus on class on the left, he means not the Marxist abstract idea of class as groups with aligned economic interests, but the specific classes Marx outlined as relevant under capitalist productive forces. Otherwise he owes us an argument as to why e.g. "black" is not a class despite its massive and identifiable role in America's economic and labor history!

Personally I am more agnostic about Marx's specific conclusions today; but if Fisher wants to call certain classes "class" but others "identitarian" I'll take his terms. But then I get to say "class is a driver of inequality" because it absolutely makes sense to say "Labor's subservience to capital is a driver of material inequality" even as it is also one type of material inequality. (Unless you think it stands so far apart from other kinds of inequality it cannot influence them at all - absolute bullshit.)

As I mentioned above, please also read Wark, where she covers in detail why she thinks Marx's analysis of extant classes is insufficient for today even as it purely pertains to labor relations.