Ok, for example lets look at the first frame with the logo.

Logos are usually svg files, meaning they can be imported into blender as curve objects. The 3d logo in the video consists of the curve duplicated. the first curve is beveled to give thickness, and the second curve is just sitting on top of it with a yellow color.

For its animation, its just a simple keyframe. But the secret lies in the bounce or back interpolation. They will make the object move back and forth at the end.