@Marklar -- Ahh, I misunderstood your question. I thought you were referring to the general experience of navigating through the story, but now I get that you are referring to the nav bar. Sorry about that!
There aren't any other layouts to choose from for the navbar at the moment. However, we recently released the ability to generate links to headings in a story. You can use this feature to manually add a table of contents in your story, which might be close to the vertical navigation you're looking for. For more details, see Add another dimension to your stories with heading links (esri.com).
We are considering other types of navigation options for the future. Could you share more information about why the horizontal nav bar doesn't meet your needs and how a vertical layout would be better suited to your story? That would help us understand what other types of experiences authors would like to provide for readers.
Owen Evans
Lead Product Engineer | StoryMaps