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I believe that TabCmd can only export the summary data from a published workbook. Though setting up a workbook as mentioned above without any filters and all the necessary fields in view at the necessary level of detail would be possible.
I also found this Tableau Idea that I believe captures the feature request for support full data export via TabCmd. Showing support for Tableau Ideas helps the product management team determine the next feature to add to Tableau Server or Tableau Desktop or Tableau Online.