Vidanon here. The only way to have a different camera angle is with a different camera. In order for this to be different "angle", it has to be a different camera. Their is no other camera "angle". It's one static (still) shot with the talent reading off of a teleprompter. In order to have a different angle, you must have a different camera.
Now, that isn't to say you can't do a zoom and scale in post-production or during a live feed. They can scale it up and change the position any which way. That said, you can't change the orientation of the camera to come in at a different angle. The angle will always stay the same. It can only be scaled and positioned (moved left, right, up or down) differently. No chance using scale and position could you make the back of that seat appear higher. Impossible. The camera angle stays the same, it can't be different.
So what is it we are seeing? Likely a green screen with a static background. Very simple to pull off, especially with a static (still) shot. No tracking necessary. This is taught in intro video production classes in high schools and community colleges around the country. The local community college has two classes that deal with this. A green screen interview is basic and simple to pull off.
Why and how did this happen? My guess is the WH sent out the feed with just POTUS in front of a green screen and the networks filled in the background, likely with supplied template background. I don't see how else this could be done.
Why? Maybe to show people how easily things can be "faked". This is basic, not hard at all but this can plant the seed of doubt in people, especially shows like Black Mirror. In the first episode with the politician and the pig they went over this extensively and that was with talent that would be moving around. This was a basic static shot.