Having worked with racing greyhounds it depends on the dogs. Some are more gamey than others and a 2 year old in diapers runninng across the yard maybe more than a male greyhound could stand or your neighbors little dog or cat ect. Some greyhound rescues do not screen well enough because not all are adoptable. And true they will run and not stop even to the point of injuring themselves. They know nothing. They are usually older dogs anywhere from 2-6 years old. Most are not housebroken. Yes they are laid back but if they fight its not pretty. So adopt only if you really love and understand the breed and thoruoughly understand where they are coming from.
They do make good pets but it takes along time to acclimate them to a home environment. Females make better pets than the males....just my experience.