^I assume "significant" means significant in the story. So offscreen characters like Spock's new captain, or bit players like Komack and Chandra in the Academy hearing or the other admirals in the Daystrom briefing, wouldn't count.
Captain Frank Abbott may have only had one or two lines, but he certainly couldn't fall under the category of "off-screen." They could easily have made Abbott a woman. I think he counts as being on the list.