Steve, just because you are an admin on a Windows 7 machine does not mean you are actively running with admin privileges. The first slide in the presentation outlines the steps you need to take. To summarize:
Exit out of LabVIEW
Find LabVIEW under Start->All Programs
Right-Click on LabVIEW
Select 'Run as Administrator'
This will apply admin rights to the LabVIEW environment. You only need to do this the first time to register the Event Log. After the Event Log is created, you can connect to it as a standard user.
Also, you can strip out all the Windows Event Viewer stuff and use the architecture with different error handling if this is too problematic.