Even though Wuthering Heights' two families live out in the middle of nowhere, they still abide by the constraints of class. Brontë lets us know through Catherine's aspirations to marry Edgar Linton that Thrushcross Grange is a far superior manor to the sprawling farmhouse at Wuthering Heights. Now, the Lintons and the Earnshaws are both members of the middle class – between the working class and the elite – as they have servants running the house. But marriage to Edgar Linton is still the means through which Catherine becomes the "greatest woman of the neighbourhood" (9.59) while, as she tells Nelly, "Did it never strike you that if Heathcliff and I married, we should be beggars? whereas if I marry Linton, I can aid Heathcliff to rise and place him out of my brother's power" (9.99).
Being an orphan with no family ties and no land, Heathcliff is the lowest on the totem pole. That Hindley denies Heathcliff an education implies that he is trying to force him to become a servant (which is how he, in fact, refers to him several times). So it makes sense that Heathcliff's revenge is tied directly to the novel's class issues, because property ownership is one of the privileges of the middle class and above. Heathcliff, in turn, seeks to punish Hindley's son, Hareton, by keeping him in a low station and denying him an education.
Heathcliff threatens Hindley's status as heir to the Earnshaw fortune, but it is ultimately Hindley's own behavior that loses him his family home.