"You get the Zoom.it short URL, an embeddable viewer, as well as the underlying DZI and surrounding metadata."
They display an embed link under the image on the short-url page, if you create one, but not for the images on the home page slideshow/demo. I agree, it's confusing and masks the functionality.
I love how the embed API is a <script> tag whose src= attribute is the URL of the zoom.it image page, with ".js" appended (and a height dimension). Love it. Very simple.