I'm not sure on an answer without additional details. How are you embedding it, is it just through a URL string that references the name of the workbook with an added tag of "?:embed=yes" ? Also, I'm not sure if there's something special associated with Tableau Public authentication or authorization to the datasource.
I had to modify the URL string and take off the suffix http:// and then I got it to render. It's a nice looking dashboard by the way.
Does the refresh of the extract work properly? I see that it uses 2 Excel datasources, and I'm not sure how TabPub manages to point at the Excel files. You may have to do something different with the Excel pointers. Generally, when I've referenced Excel files, I use an accessible UNC path and then when publishing I turn off "include external files". But it may be different because I deal with an on-premise server instead of Tableau public.