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1.
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!
by stingraytat2 November 30, 2009
 
2.
to eat out a rich woman.
i like to eat the rich.
by quazimodo October 23, 2006