The tendency to characterise Douglas Fairbanks as an acrobatic swashbuckling hero sometimes obscures the fact that he was basically a very fine comedian. Even his swashbucklers are comedies and have little in common with the later work of Errol Flynn or Tyrone Power. And his early comedies, the unforgettable Mystery of the Leaping Fish (1916) or When the Clouds Roll By (1919) are amongst his very best films.
I emphasise this because it seems to me that it is close affinity between the acting style of Fairbanks and Linder (they were also good friends) that make this very close parody such a success. Although it is true that Chaplin borrowed stylistic and sartorial tricks from Max, there is nothing much in common between their styles of comedy while there is a great deal of common ground between Doug and Max which the latter fully exploits in this delightful parody, arguably in fact a better film than the original.
Even the scenes of swash and buckle are impressive and evidently Fairbanks himself must have thought so because he subsequently employed the same Belgian fencing-master, Fred Cavens, for his own later swashbucklers.
The other US comic with whom Linder has a certain obvious affinity is Buster Keaton and both men were clearly aware of each other's films. Max's Be My Wife (1921) borrows a gag from Keaton's The Scarecrow (1920) for one of its episodes and Keaton makes a similar if less exuberant use of anachronism (here the brief appearance of the fetish top hat, the bikes, the telephone) in his own later parodies (The Three Ages and The Frozen North).
To fully appreciate L'Étroit Mousquetaire, to give it its rather neater French title, it does need to be watched in a good copy and unfortunately most of the prints available (even on DVD) are poor in quality and, more seriously still for a genre that relies on timing, lack intertitles and play at an inappropriately fast speed. There is a print of excellent quality and it is worth digging out. The version I have seen is Russian - but beware, there is also a Russian DVD version that is poor - but only currently seems to be available on youtube under the Russian title (and in cyrillic script). It is an excellent quality print, has a fair few intertitles (in Russian but, provided you know the story, this is no great problem) but, most importantly, runs at a proper speed (about 50 minutes in all) so it is really possible to appreciate what a little masterpiece this film is.