This genre of march was known as a "screamer." Screamers were lively marches (typically at a much faster tempo than would be practical for actual marching, around 130-150 beats per minute) which would get the crowd excited for the spectacle. Frederick Fennell and the Eastman Wind Ensemble put together a recording of famous screamers in 1962; you can listen to snippets of the songs here.

Among these songs is "Entrance of the Gladiators," here under its title as released in North America, "Thunder and Blazes." The original was written by Julius Fučík in 1897, and it was arranged for band by Louis-Philippe Laurendeau, a Canadian composer. He published Fučík's march in 1910 with the publishing firm Carl Fischer, on which he served as an editor (and which still exists today). From there, it got picked up by circuses around the country, and the rest is history!