Ian,
ArcGIS for Desktop 10.2 is a 32-bit program, but has a 64-bit geoprocessing "extension" that can be optionally installed.
ArcHydro Tools offers two flavors, the default 32-bit to install as an extension to default 32-bit ArcGIS for Desktop. And a version to install if the 64-bit geoprocessing "extension" has been installed.
The link noted in your error, c:\python27\arcgisx6410.1\lib\site-packages\archydrotools.pth, would be created only if the 64-bit geoprocessing and the 64-bit Python had been installed.
You'll need to back things out, and download the 32-bit ArcHydro Tools installer and use that. Or you'll need to install the 64-bit geoprocessing extension, and once that is on try the installation again.
Stuart