A dashboard is usually a collection of separate worksheets and to use the extract data button one of those worksheets needs to be selected.
If you click on a worksheet (and a light grey box around that sheet appears) does the button allow a download of data?
If not then the permissions for that user may be set to deny them access to the data.
To change permissions click on the workbook and in that workbook's page click the permissions menu:
The data permissions are this button here:
Hope that helps