Demo, Sql Server - rextester

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CREATE TABLE Yourtable
    ([datekey] int, [pointkey] int, [filter_key] varchar(4), [t_key] int)
;
    
INSERT INTO Yourtable
    ([datekey], [pointkey], [filter_key], [t_key])
VALUES
    (5506061, 37, NULL, 1),
    (5506061, 37, NULL, 1),
    (5506061, 37, NULL, 1),
    (5506061, 37, NULL, 1),
    (5506061, 37, NULL, 1),
    (5506061, 37, NULL, 1),
    (5506763, 37, NULL, 2),
    (5506763, 37, NULL, 2),
    (5506763, 37, NULL, 2),
    (45643, 97, NULL, 2),
    (45643, 97, NULL, 2),
    (45643, 97, NULL, 2),
    (45643, 97, NULL, 2),
    (45643, 97, NULL, 2),
    (45643, 97, NULL, 2),
    (1234, 83, NULL, 1),
    (1234, 83, NULL, 1),
    (1234, 83, NULL, 1),
    (1234, 83, NULL, 1),
    (1234, 83, NULL, 1),
    (1234, 83, NULL, 1)
;

;with cte as
(
SELECT datekey,
       pointkey,
       filter_key,
       CASE WHEN t_key = 1 AND Row_number()OVER(Partition by datekey ORDER BY pointkey) = 1 THEN 1 ELSE 2 END AS new_filter_key,
       t_key
FROM   Yourtable  
)
update cte set filter_key = new_filter_key

select * from yourtable

View schema
Execution time: 0,03 sec, rows selected: 21, rows affected: 42, absolute service time: 0,17 sec