First of all, "Them" is a pronoun, not a demonstrative adjective. So "Those" (which can be an adjective as well as a pronoun) should be used here instead of "Them". Also. "whiskey and rye" could be a grammatically faultless (if unlikely) reference if "rye" referred to the unprocessed grain rye or to rye meal. But when "rye" refers to a drink (as the context clearly indicates here), that drink is a type of whiskey. So when referring to drinks, "whiskey and rye" is like saying "colors and red". A more correct reference would be "whiskey including rye". But of course that would be hard-put to fit the song's meter, and arguably lyrically awkward even if it did fit metrically.