Thanks for providing such thorough repro steps, I was able to duplicate the behavior when authoring a workbook using a WDC data source in Tableau Public.
I was doing a little research and looked at the logs when the error happens, and I think I see the cause for the issue. When publishing a WDC data source to Tableau Server or Tableau Online, users need to whitelist the WDC data source so that Tableau Server can have access to refresh the data source. In this case, the Tableau Server is Tableau Public, and it's not possible for users to whitelist their WDC data sources. (see tabadmin commands ) so refreshing the workbook while it lives on the server (Tableau Public) will get an error.
Once the workbook is downloaded, the whitelisting is no longer needed, so the extract can refresh successfully. I think this behavior is expected based on the way that published WDC data sources currently work, but I think that you could file an Idea on the forum to request allowing WDC data sources to refresh on Tableau Public.
On another note, I've been enjoying looking through the data on data.world! Very much looking forward to playing with some of your data sets for my own workbooks.