What a cool video! This was a find on the Library of Congress website. Below is the description from the site.

“This most excellent picture was secured at the junction of Pennsylvania Avenue and Fifteenth Street. The parade is headed by a platoon of mounted police; next comes the Grand Marshal, Major- General Francis V. Green, and staff, as follows: A. Noel Blakeman, Lieut. Col. John S. Johnson, Major-General N.E. Thompson, U.S.A., Brigadier-General U.S.W. Day, U.S.V., Lieut. Winfield S. Overton, U.S.A., all mounted on splendid horses. Next come the famous Troop A, of Cleveland, Ohio, who act as the personal escort of the President. They present a most striking appearance as they go down the incline on Fifteenth Street, Washington. Next comes President McKinley in his carriage drawn by four of his own horses, the pair of blacks in the lead and the favorite bays on the wheel. The President is seated in the right of the carriage with Senator Hanna on the left beside him, and facing them, with their backs to the driver, are seated Representatives Cannon and McRae. Owing to special permits granted us by the United States Government, we were able to have our camera within twenty feet of the President’s carriage when it passed, and an absolutely perfect photograph was secured. The President’s carriage is followed by Secretaries Hay and Gage. The third carriage contains Secretary Root, Attorney-General Griggs and the President’s Private Secretary Cortelyou. The fourth carriage contains Secretaries Long, Wilson, Hitchcock and Postmaster-General Smith. The fifth carriage contains Lieutenant-General Miles and Admiral Dewey. We also present excellent pictures of the Admiral of the Navy and the General commanding the United States Army as they pass. This picture closes up by showing a detachment of Veterans of the Twenty-third Ohio Volunteers, followed closely by the West Point Cadets, who present a remarkable spectacle as they execute left wheel turning from Fifteenth Street into Pennsylvania Avenue. Length 125 feet. $18.75”–Edison films catalog, July, 1901, p. 8.

Below is a photo we found of McKinley in a carriage, riding through the streets of Oakland, also in 1901.