Calculando uma contagem de execução e total de execução em clientes com SQL

Você deve usar ROW_NUMBER (link ) em vez de COUNT :

DECLARE @Threshold NUMERIC(19,2)=1000; -- Use the same data type as `[AMT]`'s data type

Select
  [DID]
, [AMT]
, [Gf_Date]
--, COUNT([GID]) OVER (PARTITION BY [DID] ORDER BY [Gf_Date]) [RunningGift_Count]
, ROW_NUMBER() OVER (PARTITION BY [DID] ORDER BY [Gf_Date]) [RunningGift_Count]
, SUM([AMT]) OVER (PARTITION BY [DID] ORDER BY [Gf_Date]) [CumlativeTotal]
, CASE
      WHEN SUM([AMT]) OVER (PARTITION BY [DID] ORDER BY [Gf_Date]) >= @Threshold THEN 1
      ELSE 0
  END IsThresholdPassed
FROM [dbo].[MCT]
WHERE [SC] is null
ORDER BY [DID]