Fascinating, the falcon is treating the dog as though it were its young. I’m aware of similar behavior between Cardinals (Cardinalis cardinalis–a N. American songbird) and goldfish (see https://www.youtube.com/watch?v=qtWcb7TwClo).
My parents and we siblings raised a GSD puppy with rabbits (early 80s). Growing up with them, he got into the habit of eating their lettuce. Even after he grew up into an intimidating GSD, a big bunny would beat him up for trying to steal his lettuce. We would hear his cries and dash out running as to what hit him, only to find a bunny grabbing him by his ear and not letting go. Females were always sympathetic to him and would let him play with greens all the time.