There is actually a key there. That link is specific to the user in which has requested the file. So there is no way in which to get that link without authentication.
Only a link to it would be returned in any API. It's the application that calls it that would download it. So it your case you would be using WebClient to do this. So something like this (please note, this is outside the scope of support, so any issues would be for yourself to resolve
using (var myWebClient = new WebClient())
{
myWebClient.DownloadFile("theURLHere", "destinationFileNameHere.gz");
}
With regard the extension, could I please ensure you are using the latest release of the platform? I have seen that issue on the front end which was resolved