It appears, as his costume in the film version suggests, that he is considered a type of superhero in the Jellicle society. In the film version, Rumpus Cat is played by Frank Thompson who also plays Admetus.
In the film adaptation, it appears that he is considered a type of superhero in the Jellicle society, similar to how Rumpus Cat is played by Frank Thompson, who also takes on the role of Admetus.