The printed cards you are reading were produced by the U.S. War Department, not the Confederates. Information on them was taken from the actual Confederate rolls and registers, which are at the National Archives.

The Kentucky commands you seem to have in mind were known as Mounted Rifle Battalions, not Mounted Infantry Regiments. Infantry regiments of the famed Kentucky 'Orphan Brigade' were mounted during the last year of the war (1864-65). That's the reason for this title.