From what I've seen, this error means that the game is either accessed through an anonymous/incognito tab, or cookies are disabled on the webpage.
The engine that the game runs on requires cookies to keep track of the playthrough, so enabling them would be a fix with this and any future interactive fiction games you decide to try :)
Looking at your comment history, you have that issue with multiple different Twine games. The issue is on your end, not theirs. Downloading the game works because it's no longer a file hosted on the internet trying to access your browser information remotely, it's just a file stored on your computer.
Idrelle Games made a post addressing some common errors; yours is number one: https://idrellegames.itch.io/wayfarer/devlog/316300/troubleshooting-game-launch-...
