Declare @Table table (RowNumber int, Increment int, Score int)

Insert into @Table
values (1, 1, NULL), (2, 100000, NULL), (3, -1, NULL),
       (4, 1, NULL), (5, 10, NULL), (6, -1, NULL),
       (7, -100000, NULL), (8, -10, NULL)

Update @Table
Set Score = B.Score
From  @Table A
Join (Select RowNumber, Score = sum(Increment) over (Order By RowNumber)
      from @Table) B on A.RowNumber = B.RowNumber

Select * from @Table

RowNumber Increment       score
    1           1           1
    2           100000      100001
    3           -1          100000
    4           1           100001
    5           10          100011
    6           -1          100010
    7           -100000     10
    8           -10         0

UPDATE @Table SET Score=(SELECT SUM(Increment)
                          FROM  @Table B
                          WHERE  b.RowNumber <= A.RowNumber)
FROM @Table A