How to Chromecast videos from a Safari Books Online subscription
Instead of using the Safari To Go app, go to http://m.safaribooksonline.com and log into your account there. When you start playing the video, maximize it and the Chromecast icon will appear in the upper left. Tap that icon, select your Chromecast device, and the video will appear there. As always, you can use your Android to control volume, pause/play, and seek within the video.