Unfortunately (at least for me) it seems like it doesn't work via LAN, but somehow uses Internet connection to stream to somewhere and then back, kinda sucks and slow
Full screen streaming works beautifully for me, it's how my wife and I watch Amazon Prime movies. It's just like watching TV. I've read that the computer needs to encode the video it's streaming to the chromecast, so if your computer is slow, the streaming will be slow. That may be why you were getting poor results.