How is "Good Country People" related to Marxist criticism?
First, your thinking concerning literary theory needs a slight refinement. Saying that "Good Country People" is "related" to Marxist criticism suggests that it was written with Marxist critical ideas in mind. It suggests the writer purposely wrote something to reveal issues central to Marxism. That isn't the case.
Instead, you should think in terms of applying Marxist literary theory to "Good Country People."
If you were to apply Marxism to the story, it would be difficult to see Hulga as the proletarian. She is the educated, "wealthy" character, not Manley Pointer, although "wealthy" is relative. She is not an industrial worker, nor is she a member of the lowest working class. Thus, she is not a member of the proletariat.
If you want to apply Marxist criticism to this story, and apply appropriate roles to the characters, Manley Pointer would have to be the proletarian. And in this case, of course, he gets the better of the upper class. Hulga lives in luxury, so to speak. She doesn't really work, she has time to sit around and think, her needs are provided for, and she is pretty much a despicable human being. If Marxist theory is applied to this story, and the focus is on Manley and Hulga, Hulga is the likely target of the Marxist critic. Hulga demonstrates the shortcomings Marxists attack in people.