It's weired ! I really can't have a clear explanation of it. May be someone who lived with the people who did the movie (or their children) could have an idea. I dunno, may be also the people who watched the movie in that time (1928) directly understood what the act means.
But there is one thing that should be mentioned : we have to remember that it was just a movie. So may be it's not meant to have a real meaning.
We can't base our reasoning on a movie scene which is not real and probably not realistic, and may be a coincidence. A movie needs interpretation by its creator, to know the real meaning of its acts, not like an act of reality which is directly understood and admitted. May be if it was a reality/documentary film we could have serious thoughts about it.
May be the director wanted to represent a crazy person who talks to himself, or who is stupid enough to talk to/into a piece of something (a piece of wood or a rock), and it was meant to look funny may be. I suppose the idea of talking through a small thing was a crazy idea in that time (not like today lol) and it was just used as a joke (who knows how did jokes look like in the past LOL).
So we don't need to seriously think that one person in that time used a mobile phone/device, or really knows what mobile phones are.
Another unlikely possibility is that : it could be that, in the twenties of the last century, it was a dream that people can invent one day in the future a "wireless phone", as the wired phone was invented years ago
(since the 1870s) and may be they were dreaming to have one day a wire independent (mobile) phone as an improvement to the wired phone. You know people always dream of new inventions, like the space cars or teleportation that we see in sci-fi movies. May be Chaplin wanted to present a science fiction scene in his movie. It could be his own scientific prediction of what could happen in the future, as he was a very intelligent person. And maybe that dream of mobile phones stayed untill today when people achieved that dream.
Another possibility which is unlikely to happen too is, that a malicious person collected all the original copies of that movie and changed it with a scene newly made.