I might not have been clear. I'm saying that you should try fetching the downloadable/installable version and install the most recent version of SugarCube 2, which is v2.20.0. Then select that format, and import your file. Your file will throw an error and run in a less than ideal manner in Safari (but it will still work), and run fine in every other modern browser.
The source of the error above came from a fairly recent change in how Safari in specific handles web storage, and I believe that deficiency has since been worked around by SugarCube's most recent version. However, you cannot install SugarCube versions other than the bundled ones in the web version of Twine 2, hence why you need to grab the downloadable release.
If your story was originally written in SugarCube 2, and you do what I describe here, and then do what I describe in #1 and #2 of the original answer, this should fix the issue. It's more work than it should be, but the changes Safari implemented have broken a great deal of web apps, not just Twine, for what it's worth.
I can't guarantee this will fix it, but it seems like your problem is two-fold. You seem to have the normal importing issues and the Safari bug going on here. It's also possible that the format you used initially was actually SugarCube 1, so maybe try that first to see if it works and maybe save yourself some time. If you do, I recommend trying to get things working in Firefox first, so you don't need to worry about the Safari issue right now.