There are a few reasons for this.
First, that was a "clean" flyby, so it was going very fast with all flaps retracted. Secondly, it isn't full of passengers and baggage (as far as I know), and since it isn't going anywhere long haul the fuel load is probably also relatively low. So, the plane was fast, light, and at a low altitude. This, along with the fact that it's a 757 in the first place, means that it has amazing climb power in this video.
However, I don't believe it actually got vertical. The 757 is relatively long and people tend to think a plane is steeper than it really is. I'd say that maybe it gets up to a max of 50 degrees pitch up, although someone with a better trained eye can maybe clarify that.
Now after talking about it, I think I'm gonna go try it in flight sim...