The draft story map is over here:
Your story or some content inside it isn't shared, so I can't see it. Can you share everything publicly so I can view it to help troubleshoot your issue?
Oops! Just kidding -- I noticed that your provided a link to the story builder (with "&edit" on the end), which is why it was prompting me to log in.
I viewed your story and see what you mean. Yes, on mobile there is an "Explore" button in the lower right that you need to tap to be able to interact with your web content. This is displayed on mobile even if you choose "interaction enabled" in the media configuration panel so there's no conflict with navigating the story or the web content.
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