Because at 4:03 the tower is still there, and at 4:03 it is not. Clearly there was a section cut out.
At 4:03, they and the helicopter were still on the ground in that little park behind the world Financial Center buildings. Both towers were still up. I know this because the Marriot hotel beneath the towers was still perfectly intact at 4:03. That hotel was practically destroyed after the first tower collapsed onto it---literally cut to pieces---and then pounded into rubble half an hour later by the second collapse. Since the hotel is still there at 4:03, so is the South Tower. You just can't see it well because of the smoke and the angle.
At 4:04 the helicopter is back up in the air, not still on the ground, and the South Tower is gone. There is no footage of them getting back in the helicopter and taking off again--we don't even know how long it took. It doesn't mean anything was "cut out", it just means they weren't filming during the ascent---why would they be? It's not as if they knew when the towers were going to come down. The South tower obviously fell between the moment they got back into the helicopter and the moment they were circling above the site again. It only took about 20 seconds for it to fall, if I recall correctly. Anyway, it had obviously JUST happened in this video. The big dust cloud had barely begun to move. It covered a lot more territory before it finally began to dissipate.
Later, around 7 minutes in, one of the men says "we got out just at the right time". I think that was a statement about how close that park was to the World Trade Center. They'd have been under that cloud if they hadn't gotten back into the air when they did.
Still, there's something not quite right about this video. Maybe I should watch it again, but it's really not that interesting.