The life of the racer is pretty much all the retired dogs have known, so it shouldn't be surprising when they get excited by the approach of a cat or another small animal.
I just saw a photograph of a "hunt pot' of 3rd century Roman design found in England. There is a beautiful image of a greyhound dashing at full speed across the pottery surface. A really beautiful piece that has the typical long legs and swept back ears of the racing dog.
Because throughout its entire history the purpose of this dog was to run fast, the general shape and configuration of the body has changed very little for centuries. They appear in the art work of African and Asian buildings and in works by early painters. My thought is that since some of the early artwork is a bit on the primitive side, that it's possible the greyhound was even closer in conformation to the modern dog than was previously thought.
In 11th century England, the price of a greyhound was the same as the price of a serf. In this fashion, the greyhound was kept out of the hands of the poor and could continue to be a status symbol of the rich.
My sterling silver greyhound earrings, on the other hand, are reasonably priced and I'll bet just about anyone could afford them!