Eat The Dick as in the short name for
Richard, Like Richard Nixon A.K.A. (Tricky Dick) This means that
eat the rich refers to eat the DICK!
Also a Motorhead song (
Eat The Rich) that means just this "Eat The Dick"
C'mon
baby eat the rich, take a bite out'tha sonofabitch
Hash browns & bacon strips, I like the way that she licks her lips, c'mon
baby EAT THE RICH!