This scene of an approaching owl is not a video. It's a still image. Seriously. One still image manipulated to appear like a video scene. In fact, each scene in the following video is made from one photo only. It's unbelievable.
How did they achieve this incredible feat?
Make Productions turned still photos from the World Wildlife into a short movie that looks more like a documentary about nature shot with traditional movie cameras. Except it's not.
They processed each still photo in Photoshop, separating different elements on their own layers—parts of the background, elements of the figures, etc. Then they imported these still layers to After Effects, where they animated them in layers, moving them at sightly different speeds to achieve a parallax effect—since objects closer to the viewer appear to move faster than objects faraway, this makes your brain think the camera is moving in 3D space. It's the same parallax effect they used in old video games, when true 3D was still not available.
Then they applied some subtle deformation to some elements of the image (like the wings of that owl) to give the illusion of actual movement. Add some clever editing and boom, you think you are watching actual video captures.
I told you. Magic!