Sorry, but the people who state the airplane hits at full speed nose down are plain wrong.
1. Yes, camera lenses have distortions. However, distortion is about the same in equal radius from the centre. Meaning that an object in an upper screen would be about equally distorted as an object at the bottom of the screen for the same distance from the image centre.
2. That said, this particular lens seems a normal lens (not wide, not tele). One can draw a fairly straight line over horizon. On top of that, all the visible objects (e.g. huts) don't show any major visible distortions.
3: Given points 2 and 3, lens distortion can be ignored as it plays no role in assessing the flying path of this video.
4. As noted in point 3, the video is at an angle. An observer might get a better perception by rotating the screen to the left.
5. The airplane enters the video at about 6''.
6. Just before 7'' we can clearly see the airplane between the tree branches. It's at an angle we can't determine, but on my screen the fuselage is 26px long (only relative size matters). Wings at the root are 4 pixels long. Engines and other features are easily seen and recognisable.
7. The airplane reaches the centre of the area between upper bound of the screen and the horizon (approx. where the line crosses the central trees) at 8''. Thus, it needed 2'' to travel that distance (in 3d space, and we can't determine how fast it's moving away from us).
8. The airplane hits the ground at 11''. Seconds are not detailed enough to determine the right numbers, frame by frame analysis for which I don't have time would be needed.
9. However, it is my estimation that the plane needs about 2'' to reach the relative centre and it needs 3'' to hit the ground.
10. If the airplane was moving in constant speed on the down axis and away from us, the speed should be constant.
11: Therefore I believe the downwards speed in the lower segment is lower and the speed of moving away from camera is higher, in other words, the airplane seem to be changing the trajectory in its final moments.
12. In the final moments there's no clear view of the airplane, as it's exactly following the path the branch is hiding.
13. The airplane in this segment is much harder to see. Engines are not visible. Wings, which are clearly visible at the beginning are now just blips of interpolations. They measure 2 px.
14: Airplane is creating smaller image on the sensor either because it moved a considerable distance away from camera, or because it's pitch got higher, or combination of both.
15. At this point I would invite the reader to watch the recent video "aircraft lands at Asuncion Airport, Paraguay when staff is performing runway works". Watch closely the airplane which is approaching the camera at the landing speed. For the first 5 seconds of the video it stays virtually the same size. In fact, due to perspective humans often underestimate how fast are fast distant objects approaching.
16. The airplane would need to be moving away from the camera very fast to become that much smaller.
17: Hence, the only conclusion is, the pilots were trying to pull up, but unfortunately they did not have enough height.
Any my non factual speculation if I may: downdraft/windshear caused loss of speed while in the clouds, either pilots or systems pushed the stick forward to regain speed, lost awareness as no visual contact with the ground, once they were out of the clouds it was too late to safely pull up.