the natural lens does bulge and round out the eye, but I make them separate from the eye itself then parent it on over a flatish pupil/iris area like he has going there.
This lets you get a wet and glossy shine on the lens above the pupil which gives a feeling of depth to the eye and allows you to animate the pupil itself without changing the outer shape of the eye as a whole.
I made this eye a good while back and use it for all of my characters. It is made of two meshes and two bones. The pupil and iris area are actually completely flat with a curved lens over them.
The animation is kind of fast but:
http://www.youtube.com/watch?v=tO1RC6BRepg