It'd be a bit strange for tab streaming to go over the internet, and there certainly are apps that stream local videos. Maybe they do go over the internet, but I wouldn't just assume it.
The issue with Chromecast is you still need an internet connection to get the app onto the Chromecast to stream the video to it... I was using this and it was awesome! Then things happened and I was stuck on a shaped 256kbps connection and Videostream stopped working reliably. Switched to Kodi on the Remix Mini, works well, though not as good as Videostream did...