Nice to see all of the observations here. What I come away with, as a Chaplin fan of many years, is a continued fascination with the development of his authority as an actor and then director. TILLIE'S PUNCTURED ROMANCE (1914) was made under the great Mack Sennett and you see that Charlie is part of an all-star ensemble. The Tramp is just being born about this time. Chaplin is not the star.
By the time BY THE SEA (1915) was made he was in charge of the filmmaking, but did not have his own studios yet. He was limited by the location of the Essanay studios in southern California (he had already dismissed Chicago for the weather reasons mentioned as well as Niles/Oakland for the woodsy environment). In BY THE SEA the ensemble is one of his own making, to support him alone, a reflection of his growing stature.
A DOG'S LIFE (1918) takes this even further as at this time he is very close to completing the construction of his own studios and has a million-dollar contract with First National Pictures. The film is all about him and the dog. The Chaplin pathos is established.The fence/policemen gag is vintage, complicated Chaplin and plays out the legend of his painstakingly detail-oriented rehearsing of scenes. (His feature-length movies took years to complete.) It also shows how much of a "ballet dancer" he was, rolling back and forth under the perfectly measured hole in the fence so smoothly and perfectly! The rough edges of his music hall days were long gone.