AHA !

table-delete-row, table-insert-row are for tables in the "table.el" format like
+------------------------------------------------------------------+
|                    User Visible Entry Points                     |
+-------------------------------+----------------------------------+
|           Function            |           Description            |
+-------------------------------+----------------------------------+

Ok, this works. If i use table-insert, then table-delete-row works. Cool, thanks a lot.

But, the :
 
S-Up/Down are only for tables on the orgtbl format like
| x | y |
|---+---|
| 1 | 2 |
| 3 | 4 |

Still don't seem to work. I toggled org-support-shift-select on and off but nothing. When i do S-UP/DOWN i get the normal emacs region expanding behavior, of, if i deactivate org-support-shift-select i get a cursor movement.
That said, M-x org-table-delete-column does work. 

I gess its a binding problem …