Although not a regular member of the Algonquin Round Table, Gibbs was closely associated with many of its leading names, inheriting the job of theatre critic at "The New Yorker" from Robert Benchley in 1938. Because his years at the magazine largely overlapped with those of the better-known Alexander Woollcott, many people have confused them or assumed they were related. In fact, Gibbs was a cousin of Alice Duer Miller – yet another member of the Algonquin set – but he was not a relative of Woollcott's. On numerous occasions, in print and in person, Gibbs expressed an intense dislike for Woollcott as both an author and as a person. In a letter to James Thurber, in fact, Gibbs wrote that he thought Woollcott was "one of the most dreadful writers who ever existed." Thomas Kunkel asserts in his biography of New Yorker founder Harold Ross, "Genius in Disguise," that a profile of Alexander Woollcott written by Gibbs sparked the disassociation of Woollcott and the magazine.