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FriedlΓ€nder is talking about a specifically Nazi aspect of anti-Semitism. That's the belief in a racial hierarchy, with the "Nordic race" at the top, and "the Jews" at the bottom. It holds that everything wrong with the world, and everything wrong with people, is a result of the malign influence of "the Jews." It never goes into details about how this happens.
According to this idea, exterminating the Jews will prevent them corrupting the world any further and will allow it and its peoples to be redeemed and purified.
The Nazis did seem to believe in this. Notably, they carried on transporting victims to extermination camps when the German transportation system was breaking down under bombing attacks in the winter of 1944-45. Stopping the transports would have freed transport capacity that was needed for the armaments industry. But they carried on.