Ahhh! Right! See, the context here is important. Continuations are pretty widely known and important in the context of programming language implementation and theory, which is why I was confused by your comment. In the context where this paper was presented (to programming language researchers), making the link between delimited continuations _would_ demystify a bunch, and could allow for transferring of knowledge and techniques between the fields.

Having looked again, the authors do explain why they believe that continuations (as opposed to simply higher-order functions) are necessary. See my other comment at https://news.ycombinator.com/item?id=22347428.