The links are m3u or pls files for direct streaming to Winamp or other players. I just found that the latest Firefox was trying to save them. You have to save one, then in the Firefox download list, right click, and select "always open similar files". Then your associated player like VLC will open the stream link.

One can also review "application" in browser settings to see how file extensions are handled, and set the associated application.

Some are indeed no longer working, often because the site has gone to some non-stream-rippable in-browser player or app, perhaps for those with phones etc that are confused by advanced technology of the past, or so that they can serve up ads and tracking.