I don't think the video was shot with a mobile camera, but probably a DV camera typical of the day – Canon XL1 was pretty popular if I recall. These days you can record HD video on your cell phone, but a decade ago (and recall, the original iPhone was released just in the year prior to this video) you had to get dedicated equipment that would run in the thousands of dollars.

Camera quality has absolutely exploded in the last decade, when compared with how much they've shrunk, and Apple certainly had a role to play in that transformation. I'm not at all surprised that video from a decade ago looks so dated compared with video today.