You can't mix UPDATE joining 2 (or more) tables and ORDER BY.
You can bypass the limitation, with something like this:
UPDATE 
    pipeline_deliveries AS upd
  JOIN
    ( SELECT t.pipeline_deliveryID, 
             @i := @i+1 AS row_number 
      FROM 
          ( SELECT @i:=0 ) AS dummy
        CROSS JOIN 
          ( SELECT d.pipeline_deliveryID
            FROM 
                pipeline_deliveries AS d 
              JOIN 
                pipeline_routesXdeliveryID AS rXd
                  ON d.pipeline_deliveryID = rXd.pipeline_deliveryID
              LEFT JOIN 
                pipeline_routes AS r
                  ON rXd.pipeline_routeID = r.pipeline_routeID
            WHERE 
                d.pipelineID = 11
            ORDER BY 
                r.departure_time, d.pipeline_deliveryID
          ) AS t
    ) AS tmp
      ON tmp.pipeline_deliveryID = upd.pipeline_deliveryID
SET 
    upd.delivery_number = tmp.row_number ;
The above uses two features of MySQL, user defined variables and ordering inside a derived table. Because the latter is not standard SQL, it may very well break in a feature release of MySQL (when the optimizer is clever enough to figure out that ordering inside a derived table is useless unless there is a LIMIT clause). In fact the query would do exactly that in the latest versions of MariaDB (5.3 and 5.5). It would run as if the ORDER BY was not there and the results would not be the expected. See a related question at MariaDB site: GROUP BY trick has been optimized away. 
The same may very well happen in any future release of main-strean MySQL (maybe in 5.6, anyone care to test this?) that will improve the optimizer code.
So, it's better to write this in standard SQL. The best would be window functions which haven't been implemented yet. But you could also use a self-join, which will be not very bad regarding efficiency, as long as you are dealing with a small subset of rows to be affected by the update.
UPDATE 
    pipeline_deliveries AS upd
  JOIN
    ( SELECT t1.pipeline_deliveryID
           , COUNT(*) AS row_number
      FROM
          ( SELECT d.pipeline_deliveryID
                 , r.departure_time
            FROM 
                pipeline_deliveries AS d 
              JOIN 
                pipeline_routesXdeliveryID AS rXd
                  ON d.pipeline_deliveryID = rXd.pipeline_deliveryID
              LEFT JOIN 
                pipeline_routes AS r
                  ON rXd.pipeline_routeID = r.pipeline_routeID
            WHERE 
                d.pipelineID = 11
          ) AS t1
        JOIN
          ( SELECT d.pipeline_deliveryID
                 , r.departure_time
            FROM 
                pipeline_deliveries AS d 
              JOIN 
                pipeline_routesXdeliveryID AS rXd
                  ON d.pipeline_deliveryID = rXd.pipeline_deliveryID
              LEFT JOIN 
                pipeline_routes AS r
                  ON rXd.pipeline_routeID = r.pipeline_routeID
            WHERE 
                d.pipelineID = 11
          ) AS t2
          ON t2.departure_time < t2.departure_time
          OR t2.departure_time = t2.departure_time 
             AND t2.pipeline_deliveryID <= t1.pipeline_deliveryID
          OR t1.departure_time IS NULL
             AND ( t2.departure_time IS NOT NULL
                OR t2.departure_time IS NULL
                   AND t2.pipeline_deliveryID <= t1.pipeline_deliveryID
                 )
      GROUP BY
          t1.pipeline_deliveryID  
    ) AS tmp
      ON tmp.pipeline_deliveryID = upd.pipeline_deliveryID
SET 
    upd.delivery_number = tmp.row_number ;