I believe you have to have sold over 5,000 copies of your book to be considered a published author. So if you haven't sold that many, then for the purposes of this contest, you are considered unpublished and you're fine.
The story you are submitting must be unpublished. Peer review is okay, but if the story you are entering has been published on a website, in a magazine, or in another anthology, then it won't qualify for the contest.
Hope that helps.
