It's not quite as apocalyptic as it sounds as first:
Last.fm is retiring a feature whereby users could play any full song they like, and is instead outsourcing the feature to a range of third-party, cloud-based music services.
You can still listen to music through Last FM: it's just you can only do so now through its clunky random radio service.
So it's not quite Last FM falls silent; and pointing listeners to hear a specific track on a different service isn't a bad idea. Kind of implies that they're struggling to make enough money to cover the bandwidth costs of people having a quick, specific listen, though.