The phrase "a kind of magic" is actually used in the film by Christopher Lambert, and impressed Roger Taylor so much that he used it as inspiration for the song. There are references to the film in the lyrics: "one prize, one goal"; "no mortal man"; "there can be only one".
The music video for this song was directed by Russell Mulcahy, director of Highlander. Notable is that Brian May did not use his famous Red Special guitar in the music video, but instead a 1984 copy. In the video, Mercury is dressed as a magician type figure. He enters an abandoned theatre (The Playhouse Theatre in London) where May, Taylor and John Deacon (all dressed as stereotypical tramps) are asleep until awakened by Mercury's entrance. Mercury transforms the hobos into the Queen members, dressed regularly with their instruments, then back to hobos again as he leaves. Throughout the video, cartoon images dance to the beat of the song which was produced by the Walt Disney Corporation. As May later remembered, the theater was old and derelict, and lacking central heating, so the band were quite cold during the March filming.