I'd seen this very brief film (just about a minute long) a couple times before, and I remember chuckling. I see it again and am surprised to find myself somewhat laughing at it again. It's different for everyone, I suppose, but most of the early primitive films aren't very entertaining in themselves. In my comments on "A Trip to the Moon" (Le Voyage dans la lune) (1902), I mentioned how it was the earliest film that I found a good deal of amusement and entertainment in watching. R.W. Paul made this film the following year--the same year that "The Great Train Robbery" (1903) introduced some genuine dramatic excitement to the screen. The story film, as well as screen comedy, and the art form itself were very much in their infancy. Don't confuse my comments as discouragement from watching the early films, though. They are historically and cinematically interesting and enriching to those who take the journey.
Anyhow, the story is two men playing chess; one of them cheats, they argue and then come to blows. The painted picturesque backdrop is effective, as others have mentioned. The situation of order and intellectual activity turning to chaos and brute violence isn't very amusing in itself. The filmic innovation of having much of the fight occur offscreen, however, is quite funny. Cecil Hepworth had previously explored the comedic possibilities of offscreen space in "Explosion of a Motor Car" (1900), but I prefer this later film.
This short film is one stationary shot, but R.W. Paul also co-invented the multi-shot film, such as in "Come Along Do!" and "The Launch of H.M.S. Albion" (both 1898). Here, however, he shows the effectiveness of one shot and how to use it and offscreen space to advantage. Paul's camera may very well have been immobile, too; that is, it was likely connected to the stand so that it couldn't pan or tilt, unlike in the films of James H. White, or in "Desperate Poaching Affray" and "The Great Train Robbery".