Chrome For iOS Updated, Almost Supports Chromecast
Google has updated their iOS version of Chrome, bringing it to version 36. Among the alterations noted in the changelog are Chromecast support — sort of. The language is a bit fuzzy, and doesn't really add up to iOS support for Google's dongle at all.
A bit confusing, the changelog notes it now "allows mobile sites that have added Cast support to work with your Cast-enabled device." Cast-enabled devices are pretty straightforward and easy to grasp, but the mobile website support? Not so much.
In using the new Chrome, websites you might expect to support Google Cast don't. YouTube is a notable exception, and some Redditors have found that a workaround for Twitch.TV works — but that's about it. Nothing that would make you actually want to cast is supported.
The issue for video is that the default iOS player is used, which isn't supportive of Cast. The YouTube iOS app supports Cast, but you'll be hard-pressed to find a website via iOS that will. Google may support it in Chrome now, but they seem to be waiting on the world to support them back.
You're likely better off using apps instead of banging your head against a wall trying to cast from Chrome on iOS. If you need a list of which apps on iOS support Cast, Google has a full list available on their Chromecast page.