The famous "mirror gag" did not originate with Charley Chase and certainly not with Chaplin whose Floorwalker is only a rather vague allusion to it. It had been a vaudeville act by the Lyman brothers (twins) as early as 1900 in a review called A Merry Chase, is first (to my knowledge) included in a film by Alice Guy in His Double in 1912. It was revived as "the broken mirror" as a stage-act by the Schwartz Brothers in 1913 (possibly inspired by the Guy film) in a show called A Glimpse of the Great White Way, used cursorily (and without mirror) by Chaplin in The Floor Walker (1916)and by Harold Lloyd in The Marathon (1919).
Max Linder's use in Seven Years of Bad Luck (1921)is much more elaborate. The two persons either side of the mirror do not really resemble each other and the sequence is one part of a complex process of cause and effect that extends throughout the film.
McCarey's innovation here is the died that the mirror character impossibly copies the antics of the other, guessing each time what he will do. Here it is well done but a little rushed; the dame pattern would be repeated by McCarey in more leisurely (perhaps too leisurely) fashion in Duck Soup (1933).