At the point where you choose the texture is where I'm at.
https://i.imgur.com/wiW8Yzo.png No option to choose texture
https://i.imgur.com/FYeklVK.png No "dropdown menu" to tell Blender it's an environment texture and the node editor isn't letting me to define one (greyed out).
As you can see Cycles is enabled.
This is the previous lesson I was referring to: https://cgcookie.com/lesson/world-environment. It's the little dot button beside the color swatch for the world, that's where you'll find the environment option.