ClockworkMod Recovery developer Koushik Dutta has made some tweaks to the CyanogenMod ROM allowing you to play any video or audio file on your phone directly to your Chromecast connected TV.
Mr. Dutta has directly baked in the media playing functionality into the ROM’s framework. This means that even if the media app, be it video or audio, hasn’t yet utilized the Chromecast API, streaming would still work.
Furthermore, video and audio files from internal and external storage are supported. And here’s the actual functionality of playing any local video or audio file to your TV.
While there isn’t any information regarding availability, an educated guess would be for this Chromecast functionality to be featured in CyanogenMod 10.2 (Android 4.3). Patience is a virtue.