I don't think the book is actually arguing for a Marxist revolution. I linked to the intro to the book, and there's zero mention of Marxism, even though Marxists love their Marx. They don't hide it. They are out and proud.
Read the intro I linked to. Ninety-nine percent of books, you can get the gist form the intro and skip the rest of the book.
To some extent, he just seems to argue that if you aren't pulling on the oars fighting racism, you're dragging in the water. No middle ground. Not sure I accept that, but it's not Marxism.
He argues that capitalism is racist, only capitalism is racist, and that racism has ingrained itself into every facet of America's institutions and government. Since capitalism is the problem, capitalism must go. He argues the solution is, ironically, more government oversight and control. He doesn't invoke the term Marxism, you're right, but if it walks like a duck and quacks like a duck... He is slapping his own label on your standard Marxist revolution and pretending like it's an original thought. He is surrounding that with some additional, even more radical but admittedly original thought, like that everyone who doesn't agree with him is a racist and that the only way to fix past discrimination is future discrimination. Actually, on second thought that doesn't sound too original after all.
Or, perhaps I'm missing something, and I'd love if you could point it out. If you do, it would be especially helpful if you point to something specific in my words above that is wrong.