Spirited Away includes many different aspects of Marxist thought:
The main hub of the story is the bath house. Chihiro is told that she cannot exist in that world without working, and that she has to work for Yubaba. This doesn't sound like capitalism in the contemporary sense, where one might have some degree of choice where to work. But it fits the Marxist interpretation of capitalism as a system, with one class that owns the means of production (the bourgeoisie) and another class that needs access to the means of production (the working class) to make their living. Yubaba is the bourgeois owner, all the others are the workers who depend on her. This theme is repeated with the little magic sootballs, who have to work to stay in an animate form.
While the bath house itself can be beautiful and glowing, it is a terrifying place as well, where many forms of corruption happen:
There is Haku, who came to the bath house because he was attracted by Yubaba's power and wants to learn. Haku is a good person by heart, but he has to hide his goodness and do bad things he wouldn't normally agree with.
There is No-Face, who buys the workers' friendship by satisfying their want for gold. Insofar he is the ultimate personification of money fetishism. It seems that it is the greed of the bath house that corrupted him into this form, fitting the form of a faceless character that merely mirrors the people around him. Chihiro's conditionless friendship, without any appreciation for wealth, completely puzzles him.
There is Yubaba's giant baby, which has no willpower or opinion on its own, only it's immediate needs in sight. More about that later.
And there are Chihiro's parents, who fall into gluttony and become Yubaba's pigs, also incapable of caring for themselves. A rather typical criticism of consumerism.
The moment where all of this comes together as distinctively Marxist, is when Chihiro leaves the bath house and visits Zeniba, the good witch. Zeniba's place is the total opposite to Yubaba's. It's small and humble, but peaceful and calming.
Most importantly, a little anecdote occurs when Zeniba weaves a hair tie for Chihiro. Chihiro's friends help with weaving, and in the end Zeniba hands it to Chihiro, emphasising how everyone made it together out of their own free will. There is no payment or compensation, everyone just did it together. This is the essence of communist utopianism.
In Marxism the process in the bath house is called Alienation of Labour, in which the workers have no control over the conditions of labour, nor the product, nor their mutual relationships amongst each other. The work at Zeniba's hut in contast is completely un-alienated. Everyone pours their own bit into it. It's entirely their "own" work, done in a mutual spirit rather than forced through a hierarchy.
And what happens afterwards? Haku is his good old self. Noface stays with Zeniba, apparently in the agreement that this uncorrupted environment is best for him. But even the giant baby has totally changed and is now ready to stand up against Yubaba, instead of its old infantile state. In Marxism, that is the process of emancipation and an absolute core condition that is necessary to create communism to begin with.
Both emancipating the workers, and then sustaining a society through un-alienated labour without coercion, are obviously really lofty requirements for communism! So it might be little surprise that Miyazaki decided to forgo on a communist political vision. But even then they are still beautiful things that we can experience on a smaller scale, between family or friends or some lucky people even at work, so they will always remain a good topic for movies.