Believe me, I don't need to watch that video. I've been there ;)

A lot of development happened right before Combat Evolved got released due to Microsoft injecting a lot of money. It wasn't just an Xbox port of an already finished game. Look at the E3 2000 trailer which is pretty much what has been shown at Macworld the year before. Combat Evolved looked quite different when it came out a year later. Note that Microsoft acquired Bungie in 2000.

HALO was originally based on Myth. That is when Halo was briefly (conceptually) an RTS. It evolved into a Third Person Shooter, and finally First Person Shooter. After Bungie was acquired by Microsoft, they had a year to make their game, so they made the decision to start over from the beginning and create Halo as a first person shooter.

I watched the video. The game in that trailer could just as easily have been a tactical RTS with a cinematic camera as a FPS (note the complete absence of first-person shots).