The behavior documented in the videos (refreshing the page) could make use of session storage as well as local storage, which might buy a bit more space. But unlike local storage, session storage is not shared across tabs/windows nor persisted over browser restarts. So session storage isn't really useful for the bigger problem.
The app saves its state in whatever form it wants. The demo saves it in localStorage that is very limited. One really should look at something better like IndexedDB or WebSql (or something that hides the technical details, like localForage or PouchDB).
That's why I recommend using PouchDB to work with whatever API is available. Storage limits are harder to work around, but if your HTML snapshot weights more than 50MB (or even 1MB!) that it is a problem by itself.
