Hype output is regular HTML5 and cannot (out of the box) write to the file system (local/remote). You can do all the things a sand boxed HTML5 applications can do and some fancy stuff a PWA allows you to do (using some JS) but I'd recommend using local storage as you want to remember what the individual user has read.
There is also an extension that helps in scoping the storage to a Hype widget, page or domain. But in many cases (specially single widget Hype-Projects it isn't needed)