Based on the logic provided so far, send the mail if @Result <> ''

You could use the following parameter in your email:

@query =

'SELECT ''Process Name: '' + CONVERT(VARCHAR(25),Process_Name ,0)

+''Last Message Time: ''+ CONVERT(VARCHAR(25),Last_Message_Time,0)

FROM [ITF3].[dbo].[Process]

WHERE Process_ID IN (1,2,3,4)

AND Last_Message_Time >DATEADD(HOUR,-168,GETDATE())

ORDER BY Last_Message_Time DESC'

Don't set @attach_query_result_as_file to 1.