Android TV devices act as Chromecast receivers, so you can do the same thing on Android TV, at least with media player apps. However, I don't think there's a built-in way of transitioning state for full-fledged Android apps. Samsung's apparently been experimenting with it [1], but it's still in beta, currently only works with a few Galaxy devices, and requires apps to integrate their SDK. I'm interested to see what Apple's approach looks like.
[1]: https://play.google.com/store/apps/details?id=com.samsung.fl...