Yes, it's a real grave marker. The young Mr. Pepper's life was cut short. I wonder his story?
Source: Find A Grave, database and images (https://www.findagrave.com : accessed 27 March 2019), memorial page for Spray Pepper (1882–1906), Find A Grave Memorial no. 27615316, citing Washunga Cemetery, Newkirk, Kay County, Oklahoma, USA ; Maintained by J. Mayfield.