Even though the novel is a great romance, Brontë doesn't follow the strict guidelines of the genre: the revenge plot is just as powerful, if not more so, than the love that pulls Catherine and Heathcliff together. Without revenge as such a predominant theme, Wuthering Heights would just be a thwarted love story.
When Heathcliff cannot have the woman he loves, he turns his attention to revenging his childhood tormenter, his adoptive brother Hindley. Because Hindley never lost an opportunity to demean Heathcliff, the "gypsy" grows up determined to destroy Hindley and become master of the two houses. The fact that Hindley already has a tendency to drink and gamble to excess makes Heathcliff's vengeance all the easier.
Without this desire for revenge, Heathcliff would have had nothing to do but pine after Catherine, so revenge becomes a major motivator for his character. On paper, he succeeds in his revenge: thwarting property and inheritance laws, he manages to become owner of the two houses. But by his own admission, revenge loses its thrill in the end.
But not everyone is bitter in the novel. It is noteworthy that even though he is sorely abused, Hareton rises above it and becomes a decent person.
Though Heathcliff is driven by a desire for vengeance, he is certainly not the only character who spends energy on it.