Ah, I mean if you're running the itch client and click the "Install" button on a page with an HTML export. It just downloads the index.html and runs it when you click launch. I can't remember if local storage works in such a case.*
Now would be a good time for me to ask if there's an export for a Linux executable?
*Edit: Just tested, actually it does work. At least in Chrome browser, perhaps not in the itch browser. I'll test that now...
...aaand nope, it doesn't work in itch browser.