Since then I have found out that Dukenbai Doszhanov is indeed a Kazakhstani author, and he's been writing for a while. I guess he was Party connected -- these stories were published during the Soviet era and translated into English by a Moscow press (the date on the cover is 1979). Doszhanov (or Doszhan, the Kazakh version now used) is still a high-profile writer. He is editor of the museum journal of the Presidential Center of Culture of Kazakhstan, laureate of the State Prize of RK, a fan and resident of Astana. In 2005 he published a novel, Ak Orda, relating events in the history of Kazakhstan with the main character being President Nursultan Nazarbayev. He has written numerous novels, though I can't find reference to any in English.
The Little Jockey contains two stories, "Good Old Granddad Beknur," and the title story. In the first, a young man riding home across the steppe stops at a lonely yurta, and finds an old shepherd he had known as a child. The story ends with "There's nothing dearer to man than than his homeland and countryside."
"The Little Jockey" moves back to the childhood of that same young man.
Dalabai has been racing horses since he was six. Now he was ten and had got the hang of it. . . he had been entrusted to ride Kerkiik and defend the honor of the whole district of Karatau.Starting with "Go!" and ending at the finish line, Dalabai rides the race of his life to hear his father say," You're a worthy son of your great forefathers!"
Intrigued? You can download a PDF file (11.5 mb, with colour illustrations) of the title story here.
Duszhenov, D. The Little Jockey (Мальчик-жокей).
Translated by Janette C. Butler; ilustrated by V. Shulzhenko.
Moscow: Progress Publishers, 1979.