Adventuron games hosted on itch.io have a similar problem, except that (in my experience) they just display a blank screen with no error message. (For instance, The Familiar.)
I have a fiddly workaround for both Twine and Adventuron cases, that doesn’t involve allowing third-party cookies:
(I don’t know how stable these URLs are – probably they can’t be guaranteed not to change – but that one has been stable for a couple of months, at least.)
You can also get the url by pressing “Run game”, right-clicking on the frame, then selecting “This frame” → “Show only this frame”. (This doesn’t seem to work with the Adventuron game you linked, but it does with Twine.)