Did not see gvimext.reg in the binary, so I experimented some more. After staring at install.exe some more, I realized I had not told it to make any changes. But doing it correctly, it *still* did not update my registry!
So I then tried uninstalling and re-installing the entire vim 7.0. But again, no luck. Finally, I manually added the registry entries, as detailed in :help install-registry and that fixed the problem. (Note that the last step in the help text is out of date--it refers to vim 5.6, so I just skipped that one!)
