When I choose "Publish to File" it saves as an html document but it doesn't work on other people's computers. I've tried everything - saving to different places on my computer, doing it from both the online version and the downloaded version - but nothing is working.
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You've never saved it to your Documents/Twine/Stories directory, I hope. That's your story data directory, never publish to that directory.
If you're using the executable version, then the save as dialog should not have defaulted to your Documents/Twine/Stories directory. Even if it is for some reason, it's a standard save as dialog for your OS, so simply choose some other directory within which to save the file.
If you're using the browser-based version, then the save dialog should default to saving the file into your browser's default save location—usually, your OS' downloads directory, if it has one setup. Check your browser's options to see where that is.
The file is just information not a stand alone file. it will not work in a browser alone it has to use the Twine engine to work.
you have to turn it into an Ebook if you want it to be a stand alone working story
All the Twine 2 Story Projects that you see within the application's Stories list are stored locally on your machine (exactly where depends on what release type you are using) and not on the Twine web-server, because of this your Story projects will never automatically appear in someone else's Stories list.
There is no such thing as the "Twine engine", there is how ever Story Formats and each of these define what core features are available to an Author that uses it.
Each of the different Story Formats are a mini web-application that knows how to process the contents of a Story Project, when you use the Publish to File option to create a Story HTML file the Twine 2 application combines the selected Story Format and your Story Project's data together to produce the Story HTML file which only needs a web-browser to run, it does not need to be converted into an EBook.
so I have no idea why yours is not working