SQL Server 2017

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WITH DataTable AS (
    SELECT 1 AS RowID, 120 AS LinkID, 1 AS [Order], 1 AS Data, 1 AS DataSpecifier UNION ALL
    SELECT 2,       120,      2,      1,       3  UNION ALL
    SELECT 3,       120,      3,      1,       10 UNION ALL
    SELECT 4,       120,      4,      1,       13 UNION ALL
    SELECT 5,       120,      5,      1,       10 UNION ALL
    SELECT 6,       120,      6,      1,       13 UNION ALL
    SELECT 7,       371,      1,      6,       2  UNION ALL
    SELECT 8,       371,      2,      3,       5  UNION ALL
    SELECT 9,       371,      3,      8,       1  UNION ALL
    SELECT 10,      371,      4,      10,      1  UNION ALL
    SELECT 11,      371,      5,      7,       2  UNION ALL
    SELECT 12,      371,      6,      3,       3  UNION ALL
    SELECT 13,      371,      7,      7,       2  UNION ALL
    SELECT 14,      371,      8,      17,      4
),
cte AS (
    SELECT *,
        COUNT(*) OVER (PARTITION BY LinkID, Data, DataSpecifier ORDER BY [Order]) - 1 cnt
    FROM DataTable
),
cte2 AS (
    SELECT *,
        SUM(cnt) OVER (PARTITION BY LinkID ORDER BY [Order]) num
    FROM cte
)

SELECT *
FROM cte2
WHERE num = 0
ORDER BY LinkID, [Order];

RowID	LinkID	Order	Data	DataSpecifier
1	120	1	1	1
2	120	2	1	3
3	120	3	1	10
4	120	4	1	13
7	371	1	6	2
8	371	2	3	5
9	371	3	8	1
10	371	4	10	1
11	371	5	7	2
12	371	6	3	3

RowID	LinkID	Order	Data	DataSpecifier
1	120	1	1	1
2	120	2	1	3
3	120	3	1	10
4	120	4	1	13
7	371	1	6	2
8	371	2	3	5
9	371	3	8	1
10	371	4	10	1
11	371	5	7	2
12	371	6	3	3

RowID	LinkID	Order	Data	DataSpecifier
1	120	1	1	1
2	120	2	1	3
3	120	3	1	10
4	120	4	1	13
7	371	1	6	2
8	371	2	3	5
9	371	3	8	1
10	371	4	10	1
11	371	5	7	2
12	371	6	3	3

RowID	LinkID	Order	Data	DataSpecifier
1	120	1	1	1
2	120	2	1	3
3	120	3	1	10
4	120	4	1	13
7	371	1	6	2
8	371	2	3	5
9	371	3	8	1
10	371	4	10	1
11	371	5	7	2
12	371	6	3	3