Hot on the heels of Rudy Giuliani’s “apparently inebriated” cameo at the Jan. 6 committee hearing and “documusical” about his exploits premiering at the Tribeca Film Festival, The Daily Show is giving the man formerly misidentified as “America’s Mayor” its official biopic treatment.

In “The Dailyshowography of Rudy Giuliani: Oozing Greatness,”...