As the Associated Press has pointed out, "other synthesizers were already on the market [at the time], but Moog's stood out for being small, light and versatile." Moreover, Moog's timing was right: Bands such as The Beatles, which would eventually use a Moog machine on the album "Abbey Road," wanted a psychedelic sound, and the Moog could provide it in spades.

For more, check out this Christian Science Monitor story. Also, check out this this Youtube video about the doodle and Moog synthesizers.