Economists use the word "capital" without making reference to Marx. Marx didn't come up with that word, it had a meaning in classical economics since Adam Smith (and maybe before).
I think the rest of your post is wrong too. Marx does argue for a "mechanical determination of ideology". For Marx, man is the animal that labors, not a rational animal or a political animal. What matters is what you make with your body. If you labor with your body then you're a proletarian, and you will experience class consciousness from that perspective. If you make money from other people's labor, you're bourgeois, and you will experience bourgeois class consciousness.
I don't know if Marx talks about bourgeois who consider themselves Marxists (like Engels -- Marx was not bourgeois).
> In general I think his analysis is that "capitalism should just change some specific things to reduce inequality" without any materialist, political-economic understanding of why inequality is so rampant in the first place - why capital's dominance comes from the structure of the economy. That is why marxism is interesting, marxism makes a very compelling argument for it, and liberals ignore it at their peril.
This is also bizarre. Piketty does have a theory about "why inequality is so rampant in the first place". He just thinks we can change the laws and fix it!