Actually that is the face of a multiplayer spartan... definately not the Chief himself. Bungie stated that they will not be revealing the Chief's face even in Halo 3(We'll see if they hold true on that front)
Some people have theorized that the face was included inside the helmet in case anyone did shove the camera through the visor, like in the film. They believe this was done so that there wouldn't just be empty space inside. I have a different idea however. I have a feeling the face is there because the visor is not 100% opaque, and uses the object/texture data behind it to add depth to the visor since it will be displaying realtime relfections. Under certain lighting conditions you will probably be able to see hints of the face behind the visor. This is evident when the character in the video charges the plasma pistol.