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You must execute the code again to save those values in the database.

CREATE TABLE dog_walks (
     dog_walker_id int,
     walk_date varchar(255),
     dog_walks_count int
);

INSERT INTO dog_walks (dog_walker_id, walk_date, dog_walks_count)
VALUES (1, '2010-03-01',1);
INSERT INTO dog_walks (dog_walker_id, walk_date, dog_walks_count)
VALUES (1, '2010-03-02',0);
INSERT INTO dog_walks (dog_walker_id, walk_date, dog_walks_count)
VALUES (1, '2010-03-03',4);
INSERT INTO dog_walks (dog_walker_id, walk_date, dog_walks_count)
VALUES (1, '2010-03-04',1);
INSERT INTO dog_walks (dog_walker_id, walk_date, dog_walks_count)
VALUES (1, '2010-03-05',1);
INSERT INTO dog_walks (dog_walker_id, walk_date, dog_walks_count)
VALUES (1, '2010-03-06',1);
INSERT INTO dog_walks (dog_walker_id, walk_date, dog_walks_count)
VALUES (1, '2010-03-07',3);
INSERT INTO dog_walks (dog_walker_id, walk_date, dog_walks_count)
VALUES (1, '2010-03-08',0);
INSERT INTO dog_walks (dog_walker_id, walk_date, dog_walks_count)
VALUES (1, '2010-03-09',0);
INSERT INTO dog_walks (dog_walker_id, walk_date, dog_walks_count)
VALUES (1, '2010-03-10',6);

SELECT 
	dog_walker_id,
    walk_date,
 	SUM(COALESCE(dog_walks_count,0)) OVER (PARTITION BY dog_walker_id ORDER BY walk_date ASC ROWS BETWEEN 7 PRECEDING AND current ROW) AS "7_day_sum"
FROM dog_walks;

dog_walker_id	walk_date	7_day_sum
1	2010-03-01	1
1	2010-03-02	1
1	2010-03-03	5
1	2010-03-04	6
1	2010-03-05	7
1	2010-03-06	8
1	2010-03-07	11
1	2010-03-08	11
1	2010-03-09	10
1	2010-03-10	16

(1 rows affected)

(1 rows affected)

(1 rows affected)

(1 rows affected)

(1 rows affected)

(1 rows affected)

(1 rows affected)

(1 rows affected)

(1 rows affected)

(1 rows affected)

(10 rows affected)