This may be too late to be helpful to you, but I hope it will be helpful to others.
First, in my short experience with epub.js I have wrestled with the same question, and eventually learned that if you want to set the height and width options to "100%", as suggested in the "Getting Started" guide on the README you reference, and as you use in your example, the element you are rendering to must have a fixed height. In your case, the #area div. Try experimenting with setting the CSS for #area to height: 500px;, and seeing if the epub then renders.
This is somewhat more informative epub.js documentation, but not really about set-up: http://epubjs.org/documentation/0.3/#rendition
Second, this may not be the issue for you at all, I know the README instructs referencing <script src="../dist/epub.min.js"></script> exactly as you have it, but for my purposes in a Rails 5.1 application with Webpack, that did not work.
Instead I added it to the project with Yarn (yarn add epubjs, or npm install epubjs if you use npm), and then imported it into the relevant file (in my case a Vue component) with import ePub from 'epubjs'.
You can check if you have epub.js loaded by console logging your book or rendition variables after you define them (console.log(book) or console.log(rendition), in your example). If they are objects chock-full of fancy functions unfamiliar to you, you'll know you've got epub.js on the page, and the issue is more likely the height/width values.