The obvious inspiration for this short film is Georges Melies' 1903 A TRIP TO THE MOON, but while Melies based his movie on a Jules Verne novel, this clearly is based on H.G. Wells' FROM THE EARTH TO THE MOON -- with the names rubbed off and the site of the action changed to avoid lawsuits.
Even though we see the same sort of mix of stage and movie magic that Melies used, the purpose has shifted subtly from being special effects that the audience would gape at, to special effects that are used to get from plot point A to plot point B. When chairs float in the air, it is not to frighten and bewilder the audience and the movie's character, but to illustrate the invention of anti-gravity. When the scientist flails about while seeming to fly through outer space, it is to get to Mars. Special effects are no longer the point of the movie. They are part of the grammar.
To the modern eye it may look abrupt, but Edison had its own style of editing that it would use until 1913. There were few screen titles used at Edison.
Director Ashley Miller seems to have used Edison as a source of income and after they stopped production, gave up the movies. He seems to have had a real career acting and directing on Broadway.