Chromecast runs an app inside that does the streaming. Phone/tablet just setup the URL for the stream. You can easily verified this by setup the chromecast to

Chromecast runs an app inside that does the streaming. Phone/tablet just setup the URL for the stream. You can easily verified this by setup the chromecast to stream from youtube with a phone after it start play, you can turn off the phone and and it would still be playing. The phone/table for chromecast is just a fancy remote control.