If you read what you linked, the meaning where they overlap is in the sense of a tail or something hanging down. The cue in the sense it’s used here, as a prompt to act, was in use since the 1500s in theater. The use of queue to mean a line only began in the 1800s and probably came out of the now basically unused meaning of cue/queue to refer to a tail-like thing. Curly cue and pool cue are the only remaining uses I can think of. Queue has basically lost that meaning in favor of its new one thanks to IT applications.