Little is known about the world's first cat video, other than that in 1894, Thomas Edison filmed two cats boxing. This amazing clip was discovered in July 1984 in his New Jersey studio.

From Public Domain Review:

The performance was part of Professor Henry Welton’s 'cat circus,' which toured the United States both before and after appearing in Edison’s film. Performances included cats riding small bicycles and doing somersaults, with the boxing match being the highlight of the show. As for why the cats were filmed (apart from being an early example of people enjoying footage of cats), it might have possibly been a publicity stunt to advertise the show.