Dolly Parton, George Jones, Alabama, Waylon Jennings, Willie Nelson, and Kenny Rogers are shining stars in country music history. And 1980 was a climatic year of career-making songs for each of them.

Kenny Rogers scored the defining hit of his career when he released “The Gambler” in 1978, but he was not the first artist to record the song. Another well-known star cut it before him, and another ...