I believe the main problem is because it appears you have the click-to-run version installed. This means that winword.exe is actually not installed for those versions by design as click-to-run runs Office applications virtually.
That said, I imagine you downloaded a trial or beta version to test this in 2010 and ran into this problem.
Click-to-run versions of Office come with trial, beta, Starter Editions of Office, Office Home & Student 2010 and for Office Home & Business 2010 when you download directly from Microsoft.
Click-to-run is only available as download not with a disk. Therefore the retail version of office is a perpetual version of office suite with normal installation.