As someone that has a Windows Phone and uses Cortana, yes. Everything he was doing is a pretty standard response or action from Cortana.

I mention this every time, but I think the most interesting thing about it is that developers can integrate their apps with it. For example, you could open Cortana and say "Send a Yo to John Doe" or "GenericBankingApp, transfer $25 to my checking account".

I've been meaning to sit down and build a couple small apps that take advantage of this, but I haven't gotten around to it yet.