The answer is to use 1 PRECEDING, not CURRENT ROW -1. So, in your query, use:

    , SUM(s.OrderQty) OVER (PARTITION BY  SalesOrderID 
                            ORDER BY SalesOrderDetailID
                            ROWS BETWEEN UNBOUNDED PRECEDING 
                                     AND 1 PRECEDING) 
    AS  PreviousRunningTotal

Also note that on your other calculation:

    , SUM(s.OrderQty) OVER (PARTITION BY  SalesOrderID
                            ORDER BY SalesOrderDetailID) ...

SQL-Server uses the default ^* RANGE UNBOUNDED PRECEDING AND CURRENT ROW. I think that there is an efficiency difference and ROWS UNBOUNDED PRECEDING AND CURRENT ROW is to be preferred (after testing of course and if it gives the results you want).

Much more details you can find in the blog article by @Aaron Bertrand, including performance tests: Best approaches for running totals – updated for SQL Server 2012

^{* this is of course the default range when an ORDER BY is present inside the OVER clause - otherwise, without ORDER BY the default is the whole partition.}

I tend to use outer apply or a correlated subquery for this purpose. The equivalent to your original query should be:

select daw.BranchNo, daw.FiscalWeek, daw.SalesExVAT,
       (select Sum(daw2.SalesExVAT)
        from [EUUKSQL01].[DASHBOARD].[dbo].[SalesAggregateWeek] daw2
        where daw2.BranchNo = daw.BranchNo and
              daw2.FiscalYear = daw.FiscalYear and
              daw2.FiscalWeek <= daw.FiscalWeek
       ) As cumulative_sales
from [EUUKSQL01].[DASHBOARD].[dbo].[SalesAggregateWeek] daw
where daw.BranchNO in (1, 4, 7) and daw.FiscalYear = 2017;

This assumes that the BranchNo/FiscalYear/FiscalWeek combination is unique in the table (which seems like a reasonable assumption).

It's the "frame" or "range" clause of window functions, which are part of the SQL standard and implemented in many databases, including Teradata.

A simple example would be to calculate the average amount in a frame of three days. I'm using PostgreSQL syntax for the example, but it will be the same for Teradata:

WITH data (t, a) AS (
  VALUES(1, 1),
        (2, 5),
        (3, 3),
        (4, 5),
        (5, 4),
        (6, 11)
)
SELECT t, a, avg(a) OVER (ORDER BY t ROWS BETWEEN 1 PRECEDING AND 1 FOLLOWING)
FROM data
ORDER BY t

... which yields:

t  a  avg
----------
1  1  3.00
2  5  3.00
3  3  4.33
4  5  4.00
5  4  6.67
6 11  7.50

As you can see, each average is calculated "over" an ordered frame consisting of the range between the previous row (1 preceding) and the subsequent row (1 following).

When you write ROWS UNBOUNDED PRECEDING, then the frame's lower bound is simply infinite. This is useful when calculating sums (i.e. "running totals"), for instance:

WITH data (t, a) AS (
  VALUES(1, 1),
        (2, 5),
        (3, 3),
        (4, 5),
        (5, 4),
        (6, 11)
)
SELECT t, a, sum(a) OVER (ORDER BY t ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW)
FROM data
ORDER BY t

yielding...

t  a  sum
---------
1  1    1
2  5    6
3  3    9
4  5   14
5  4   18
6 11   29

Here's another very good explanations of SQL window functions.