I thought the same too before I watched the video, but they said there's no "Edit" button in the bottom left hand corner to show it was the co-op building. I guess they could be hiding the Edit button though.
My guess is that you initiate this style of multiplayer using this button here (circled in picture)?
You select a course that you've made or downloaded, hit that button, then you go into a menu to select your characters and start playing in single-screen multiplayer?