So here's the challenge. How would you listen to http://ntslive.co.uk/ via Chromecast?
Dig around and you'll find the listen.pls file. In there you'll find a stream, http://stream-relay-geo.ntslive.net/stream which appears to play in a chrome tab. So you could then cast the tab, or maybe even re-purpose one of the Chromecast API example programs so it actually played in the Chromecast not by being streamed across from the laptop.
That's all a bit of a hassle. So is that Google's problem or NTS' problem? What about with Cast For Audio, because playing an internet radio station feels like a pretty strong use case.
At which point, I feel like Google should provide an official and supported solution to de facto standards like Shoutcast rather than expecting 3rd parties to support it.
At least if I was a middle manager in the Chromecast support group in Google, that's what I would do. ;)
I've also had some problems with buffering with Shoutcast Audio radio streams which seem to come down to limitations in the HTML5 audio tag.
You could try using Tunein, but they don't yet have Chromecast support in their web version.
Although Tunein does know about NTS.
http://tunein.com/radio/NTS-Radio-s150238/