Where does it say anything about realism?
The militant anti-communism part. Nixon was the ultimate realism and he was making detente with the communists (better for US interests).
Read the next paragraph as well:
Over the past quarter century, the neocons have sought, with increasing success, to rid the Republican Party of its isolationists, its anti-imperialists, and its realists. The younger neocons, such as William Kristol (son of Irving) and Elliott Abrams (son-in-law of Norman Podhoretz and Midge Decter), have promoted a new right-wing internationalism that holds that America should be both a global cop and a global missionary for freedom.
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