"Marxism" is the combination of the theory of dialectical materialism and the practice of revolutionary socialism. "Common sense" of modern society - including the crude and warped caricature of Marxism known as Stalinism - sees the material world and the world of ideas as distinct and independent. This is one of the reasons why hypocrisy and lies are such a defining feature of modern ruling classes. Some subsets of the infosphere, on the other hand, assert that material nature is subservient to the idealist, narrative or spiritual realms. Out of this comes all manner of religions, from Scientology to neoconservativism.
Marxism, on the other hand, see concrete and abstract realities as a dynamic, ever-changing unity, with the material world as the first and last but not the only reality. The Marxist method works on a dynamic of concrete->abstract->concrete - precisely the same, I am interested to note, as the Maat current, despite their founder's rather glib dismissal of "Marx-Leninism".
Marxism used to be often described as "scientific socialism". This phrase has fallen into disuse, corrupted by its application to the dull, mechanical materialism (backed with messianic phraseology) of Stalinism. Stalinism, as we all know (*cough*Lysenko*cough*) was pretty fuckin' far from scientific. Modern descendents of Stalinism, like the Cuban government, betray this heritage when they talk about "moral education" about the joys of working hard and living frugally as the key to inoculating their populations from the images of material abundance promised by Western propaganda. I dunno about you, but I'm sufficiently old-fashioned that I still like Marx's original vision that socialism would mean a higher material quality of life for the vast majority.
I also want to reclaim what the greenies sneeringly refer to as the "Promethean" myth at the heart of Marxism - the idea that the aim is "man's power over nature" - or, to put it in a more hippy-friendly idiom, the sovereignty of consciousness over mechanical matter and social egregores. Knowledge is power - to be able to control what's real you need a damn firm grasp of what is real and what is the "common sense" of your personal and social reality-tunnel. That's the basis of the scientific method. Most modern Western occultists seem to have given up the search for "what is real" and confined themselves to looking for a new and more fun religion. Well, to hell with that.
Chaos Marxism calls for a firm commitment to what both Marx and Crowley would have recognized as science - dismissal of all myths, firm concentration on what forms of belief and systems of knowledge enable you to measurably and predictably cause changes in material and objective reality. Everything has to begin and end in the $2.99 material world (what the Maatians call "Level 10"), and if you're not doing that, you're not doing real magick, you're just astrally wanking. The reality-tunnels of middle-class Westerners who can afford to patronise occult bookstores are not the measure of success, but the thousands of millions of people living in poverty and oppression on this planet, and the ecological sustainability of human civilisation itself. (I do note that since the ecological question came up in pressing fashion, the hard core "there is no significant objective reality" crowd seem to have shut up a bit. Nothing is designed to ensure your belief in gravity more than falling out of a plane.)
I do note, in passing, that the CM aphorism that "nothing is more fatal to magickal success than a magical (i.e. idealist) worldview" is shared by Don Webb of the Temple of Set (we thought of it independently, honest!) And here's a good article giving solipsism a slapping, from a guy who's written a book on Pop Culture Magick that I really have to buy.