This definitely seems like a very useful capability, but as the article states, the service is presently swamped with requests for downloads. So it might be a good idea to wait until the newness of the service wears off before trying it out yourself.
Website Downloader is a relatively new service that enables you to download individual pages or entire archives of websites on the Wayback Machine site. The Wayback Machine, part of the Internet Archive, is a very useful service. It enables you to browse website snapshots recorded by the site’s crawler.