What's the correct syntax for this Postgres query in MySQL?
It can be

UPDATE items, ( SELECT 1 id, 12 position UNION ALL 
                SELECT 2   , 13          UNION ALL
                SELECT 3   , 11                    ) i_vals
SET items.position = i_vals.position 
WHERE i_vals.id = items.id;


or:

UPDATE items
       JOIN   ( SELECT 1 id, 12 position UNION ALL 
                SELECT 2   , 13          UNION ALL
                SELECT 3   , 11                    ) i_vals
       ON  i_vals.id = items.id;
SET items.position = i_vals.position ;