I've seen plenty of other Twine games that do have an option for hard save files. Is that a plugin, newer version or not Twine to begin with?
Viewing post in Enter the Expansion Mansion comments
I'm by no means an expert on Twine or HTML, but, within Harlowe (the Twine coding language I'm using), the save options are limited to the browser cache. It's entirely possible that other games are able to do a hard save using Sugarcube or some other Twine language. I don't know enough about those languages to confirm or refute, though.