Sql-server – ROWLOCK in sql server

I have a table to update with no indexing in the where clause so I use ROWLOCK in the update script, hoping to get row lock instead of table lock but no luck.. so what is the function of the ROWLOCK then? I was using it in the select statement but still locking the entire table… so annoying!

DBCC TRACEON (-1, 3604, 1200)

BEGIN TRAN

UPDATE [Order]

with (ROWLOCK)

SET ProductId = 3

WHERE CustomerId = 1

TRACE OUTPUT:

DBCC execution completed. If DBCC printed error messages, contact your
system administrator.

Process 54 acquiring IX lock on OBJECT: 16:229575856:0 (class
bit2000000 ref1) result: OK

Process 54 acquiring IU lock on PAGE: 16:1:196 (class bit0 ref1)
result: OK

Process 54 acquiring U lock on RID: 16:1:196:0 (class bit0 ref1)
result: OK

Process 54 acquiring IX lock on PAGE: 16:1:196 (class bit2000000 ref0)
result: OK

Process 54 acquiring X lock on RID: 16:1:196:0 (class bit2000000 ref0)
result: OK

Process 54 releasing lock reference on RID: 16:1:196:0

Process 54 acquiring U lock on RID: 16:1:196:1 (class bit0 ref1)
result: OK

Process 54 releasing lock on RID: 16:1:196:1

Process 54 releasing lock reference on PAGE: 16:1:196

(1 row(s) affected)