Matty,
Once downloaded, what is the mechanism for either accessing or
reinstating the data?
The .mbox content (inside the .zip file) is plain text, so you could open it with a plain text editor such as Notepad (on Windows). But what you see that way is a "View Source" of all the messages, one after the other. Which is not very easy to navigate or use, but you can search it and copy out text.
To see it in a more useful form you need a program designed for reading email, such as Thunderbird. Thunderbird doesn't make this process easy, it doesn't have an "import" method for .mbox files, you either need to install an add-on or put the file in a folder under Local Folders in Thunderbird's internal data structures. Perhaps some other email readers make it easier.
There is no process for reinstating the data at either Groups.io or Y!Groups, though support at Groups.io may be able to do that for you. It is possible that other mailing list services or software could accept an .mbox file and make a new list archive from it.
Shal
Shal Farley