There is something to be afraid of with Eagles, Hawks, and Owls. I've got two hawks living in my back yard so we're really careful with Reesie.
But, watch that video again. It was staged. The eagle is sitting on the shoulder of a man in the very start of the video. They turned the fawn loose and then the Eagle. It was trained to do that. It would carry off a Yorkie very easily but that video makes me sick. Check this page out, third paragraph--
Golden Eagle