This 1894 film, one of the earliest produced by Thomas Edison's Black Maria movie studio, features two cats boxing. Obviously it's not actually a video, but it's certainly evidence that even at the dawn of cinema, over a century before YouTube, cats ruled the moving image.
But is this the first recording of a cat in motion? That credit, it seems, goes to Eadweard Muybridge for his animal locomotion studies, which include this 1887 motion study of a cat running, below. Muybridge pioneered motion capture by inventing a setup of multiple cameras in sequence, which recorded continuous movement, frame by frame.
Animal Locomotion, Plate 719, courtesy of the Boston Public Library
For more films from the Internet Archive, visit http://www.archive.org/.