Although far from perfect, I think the scene makes sense of why the Engineer ripped David's head off. He only does so after Weyland rants about living forever, being a god, and creating David. The Engineer also sees Shaw get hit in the stomach...so within seconds after meeting humans he witnesses violence, arrogance, and greed. Ripping David's head off was a direct F*** you to Weyland's arrogance.
I think the scene is important because it makes the Engineer's drive to kill the rest of the humans and complete his mission on earth less slasher film, and more in line with the idea that mankind brings violence with them wherever they go. The Engineer saw nothing good when he was awakened. If anything, everything he saw confirmed his need to wipe out humanity.