Can the sorting from an ORDER BY statement be saved explicitly with only one UPDATE statement?
UPDATE
   T1
SET
   position = T2.rn
FROM
   myTable T1
   JOIN
   (
   SELECT
      id,
      ROW_NUMBER() OVER (ORDER BY position) AS rn
   FROM
      myTable
   ) T2 ON T1.id = T2.id


Note: the order of "Keyboard" and "USB cable" is arbitrary. They both have position = 0

To tie-break positions based on item, add a secondary sort

      ROW_NUMBER() OVER (ORDER BY position, item) AS rn


If you have duplicate position,item pairs this will be arbitrary too...