Faulkner's Abner Snopes is a man who see threats everywhere he turns and who feels justified in lashing out at those threats in the most violent ways he can. Nixon is often viewed as highly paranoid, and highly vindictive, and is in that sense very Snopesian (which is to say, very much like Snopes). However, Snopes is quite a complex figure whom his son is able to empathize with, and even sometimes admire, something that many would say is true of Nixon as well.
On the negative side, Nixon is regarded by many as one of the most abysmal presidents the U.S. has ever had, and, besides extending the widely unpopular war in Vietnam and being forced to resign in disgrace after Watergate, he could be quite nasty. He did not ignore his enemies, whether real or perceived--he sought to destroy them, because he took all opposition very much to heart. It often seemed that he did not see his opponents as politically motivated, but rather as motivated by personal animus (which the quote you cite clearly suggests). He thought of himself as a man of the people, and regarded academics and student anti-war demonstrators (again, refer to the cited quotation), as well as the press corps, as elitists and snobs who had no respect for him personally. Snopes, likewise, has a special disdain for those whose station in life is above his. He sees himself as a warrior for his kind (he is a tenant farmer), a sympathetic quality, but he cannot control his rage, and acts in very cruel and stupid ways--burning barns (he is a serial arsonist as well) and making his family help him, for example.
On the plus side (IMO) for Nixon, he did meet with Chinese and Soviet leaders, create the EPA, and expand the social welfare state (he even proposed universal heath care) in a way that complicates any easy assessment of his legacy. He is widely reviled, but he was a talented politician and a fascinating historical figure. Some have said Shakespearean; apparently some say Faulknerian (or Snopesian).
Having said all that, though, my guess is that, in the quote that you have cited, Morse is focusing on the negative qualities that Snopes and Nixon share (paranoia and thugishness), not on their complexity.
Here is a link that descibes Abner Snopes.