I do not see where the WWI Card indicates he was born in MO. The GA Death Index for Henry A. Mayer d. Jan 22, 1942 has age 71 which equals b. 1870/1871.
I found listed on the 1900 Military and Naval Forces Census for Cuba, Hamilton Barracks District 107; Company or Troop: "A", Regiment: Second, Arm of Service: Cavalry. Henry A.I. Mayer, Pvt, age 26 b. Sept 1873, white, male, single, U.S. Residence: 2413 North 13 Street, St. Louis, MO. Born Arkansas, father-Germany, mother-Georgia. Can read, write and speak English.