Google Docs have been merged into Google Drive. Consider Drive as an overlay that just maps your previously existing Docs collection to your local hard drive. Since neither Word nor other applications have a way to edit Google Docs documents on the fly (plus the fact that there's no API for this), the only way to represent those documents on your local computer is to show them as .gdoc and .gsheet files.

To edit them, you still have to use the Google Docs website.

To view them, use the Docs offline mode^beta. Click the settings button, and enable it from there.

Then download the Google Docs app for Google Chrome. After all, you still need a browser though.

When you have an HTML file in Google Drive and ask to open it with Google Docs, there's no 'convert' option AFAICT and you get a 'view source' sort of view instead of seeing it rendered.

If you have the HTML file saved locally and you upload from the Google Docs page itself, there is a 'convert' option in the upload dialog, and that will produce a rendered version of the page. In my limited experience with that conversion step (importing some HTML produced by the ASCIIDoc formatter), the rendered HTML didn't look very good -- it came out with an awful-looking font and lost some formatting from the original HTML.

The top-rated Google search results for importing HTML into Google Docs all seem to assume you're importing HTML data into a spreadsheet.

So while it seems to be possible to get some kind of rendered HTML by going through one specific path, this doesn't appear to be a high priority for Google Docs.