Based on the information from the Insert custom HTML, CSS, and Javascript and Upload existing web pages support pages as well as a little Google searching, it appears that you will need to host your Story HTML file somewhere other than the Google Site itself and then use a Include gadget (iframe) to embed the hosted HTML file within one of your Google Site pages.
That widget can be access via the Edit Page -> Insert -> More Gadgets -> Featured menu items, and then by scrolling down the list and selecting Include gadget (iframe)
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That widget can be access via the Edit Page -> Insert -> More Gadgets -> Featured menu items, and then by scrolling down the list and selecting Include gadget (iframe)