I think the issue is that the Inv-AeX_AM_Monthly_Summary table has multiple rows per machine, based on the "Month Year" column (which I still don't quite get the usefulness of).  So you have to filter them out and get only the most recent month.  Try the following:
 

SELECT 
 vComputer.Name, vComputer.[User], vComputer.[OS Name], vComputer.[IP Address], vComputer.Domain,
 MAX(Inv_AeX_AM_Monthly_Summary.[Last Start]) AS [Last Start],
 DATEDIFF(day, MAX(Inv_AeX_AM_Monthly_Summary.[Last Start]),GETDATE()) AS [# of Days Last Used],
 SUM(Inv_AeX_AM_Monthly_Summary.[Run Count]) AS [Run Count],
 SUM(Inv_AeX_AM_Monthly_Summary.[Total Run Time]) AS [Total Run Time],
 Inv_AeX_AM_Monthly_Summary.[Product Name], Inv_AeX_AM_Monthly_Summary.[Product Version]
FROM   vComputer
INNER JOIN Inv_AeX_AM_Monthly_Summary
 ON vComputer.Guid = Inv_AeX_AM_Monthly_Summary._ResourceGuid
WHERE Inv_AeX_AM_Monthly_Summary.[Product Name] LIKE N'Microsoft Visio%'
 AND DATEDIFF(day,Inv_AeX_AM_Monthly_Summary.[Last Start],GETDATE()) > 30
GROUP BY vcomputer.name, vcomputer.[User],  vComputer.[OS Name], vComputer.[IP Address], vComputer.Domain, Inv_AeX_AM_Monthly_Summary.[Product Name], Inv_AeX_AM_Monthly_Summary.[Product Version]

 
Also, there is a concept in SQL called "aliasing" which allows you to use a short name (alias) for a table instead of typing out the whole name.  For example when i use vComputer view, I alias it as "vc", or Inv_AeX_AC_Identification as "acid".  YOu just put it after the table/view name:
FROM vComputer vc   --OR--  FROM vComputer AS vc. 

The "AS" is optional but helps readability.