In the official android documentation it says - "With the remote display APIs, your sender app can now render directly to any Cast receiver, like a Chromecast". What does directly mean here? Does it mean no wifi media channel is required/i.e. the chromecast device and the phone/tablet don't need to be on the same wifi network?
Yes, the do need to be on the same wifi network. Remote Display enables you to have a View in your Android app on your phone and mirror that view on your chromecast screen.