As far as I can see, Db3 does support "date format" with a 'D' char after the attribute name. I had an hex look with Neo to the dbf file I sent, you can see that it's a Dbase '3' and that there is a 'D' after cl_creadat. That's likely why Qgis table manager plugin recognizes also it as Date.
http://www.fileformat.info/format/corion-dbase-iii.htm
http://web.archive.org/web/20150323061445/http://ulisse.elettra.trieste.it/services/doc/dbase/DBFstruct.htm
Date field types are now supported in our Shapefiles, and properly filled when converting from an OgrLayer (using GetBuffer).