Funnily enough, in this definition both ML's and Anarchists fall into the same trap, and that is ignore commodity production which is the fundamental atom of capitalism. You can centralize or decentralize production all you want, give ownership to the workers or the state - this doesn't matter as long as commodity production (production for exchange) and everything that it implies remains.
After all, capitalism IS generalized commodity production, it's what automatically implies markets, production for profit, money, etc...
Also don't confuse Marxism with Marxism-Leninism, as the latter is merely a "synthesis" created by Stalin that falsified both Marx and Lenin to suit the nationalist counter-revolutionary USSR direction of development. Both Marx & Engels opposed "Socialism in one state", fought against the idea that "commodity production is socialism actually" or the stageism that is anti-materialist