Is Chrome actually decoding the file then reencoding it / pushing raw video frames, or is it just streaming the file to the Chromecast? I suspect the later.
Tried it myself. Chrome plays the video fine itself. Trying to cast that tab to Chromecast has the CPU usage on the casting computer spike way up. This is not a network bandwidth issue.
Incidentally I've just discovered that my Roku can have local videos streamed to it from my S3. It works flawlessly.
Maybe I'll try that myself later.