As indicated in the comment, I think that this is a simpler formulation of your query:
SELECT
ROW_NUMBER() OVER (
ORDER BY DATEADD(minute,DATEDIFF(minute,0,DateOfMeasure),0)) AS RowNum,
DATEADD(minute,DATEDIFF(minute,0,DateOfMeasure),0) AS 'Date'
from Data emd
Does it also exhibit the same strangeness?