Since DWCS6 and later no longer offer any kind of import functionality for the GL .site files, there's no sense in making the file "readable" in DW by adding its extension to the list. It would only open as code, not in any "meaningful to Dreamweaver" way.
You'll have to create a Dreamweaver Site Definition manually from your existing website files.
Define a site
To add to Jon's reply and Preran's explanation of what the .site file contains, and a quick read of the .site file definition. It apears that it is a parameter file, and looking at the output from the example you posted it is saved in a binary format which would require a specific program that interpretates the file into a readable format.
Even if Dw did interpretate the file, This would not help you to work with the site in Dw, as it is nothing more than a site manifest file listing all files and assets associated with the site, and how go-live should display them. As Dw would never update this list, it would become outdated after the first site edits.
Your best solution would be to create a new site definition in Dw, (follow the instructions in the link posted by Jon) then 'get' the actual web files from the server in order to work with them. It will not be simple to convert the files created by go-live to that of a W3C spec site, as go-live created and used a lot of go-live specific code for many of its features, that are not editable without using go-live.
If you do not know how to code, or wish a more visual method of creating a site, then Muse would be a better option than Dw.