As noted in the brief video above, it's because that was the first song ever "sung" by a computer voice. As noted here, from an MIT website,
"Mr. Stork played a recording that author Clarke heard at Bell Laboratories in 1962 of an ILLIAC computer singing "Daisy," which HAL sings in the movie (the voice was Canadian Shakespearean actor Douglass Rain). "It's amazing," Mr. Stork said. "In the film, it's sung in the same key."A full recording of computer speech from 1963 is HERE. Thanks, Reddit.