You need check the YouTube app or Netflix app. The casting is handled by individual apps. There are no extensions (Chrome for Android does not support extensions or apps yet).
If you want to enjoy local media (your own collections), you may check this guide: https://allaboutchromecast.com/chromecast-how-to-guide/comparison-of-5-methods-for-streaming-local-media-files-to-chromecast/
If your tablet is Note 10.1 2014 edition, you may cast the whole screen from Chromecast app, as discussed in this post: https://allaboutchromecast.com/screen-mirroring-with-chromecast/