That error message means exactly one thing: 3rd-party cookies are currently disabled—for whatever reason.
Most story formats use the Web Storage APIs for various needs. Unfortunately, all browsers gate access to Web Storage via the same controls that handle 3rd-party cookies, so disabling the latter also disables the former.
What this means for you is that either your browser has 3rd-party cookies disabled, in general or for the specific origin you’re using, or you’re attempting to run the game in a private browsing mode.
It could also be that your browser’s local storage is full, so you may need to clean up your “file://” storage (which will cause you to lose your saves).
While that can be an issue, it would come up as a different error.