Thanks for the links. Those links made it clear:
Note: If you are familiar with R Markdown, you might expect RStudio to save an HTML version of an interactive document in your working directory. However, this only works with static HTML documents. Each interactive document must be served by a computer that manages the document. As a result, interactive documents cannot be shared as a standalone HTML file.
This is the confusion I had.
But it sounds like if I install Shiny server and host the app there on the same server where I host RStudio, I can link to an app on my server and use an iframe to show the app in an html site built with Markdown.