Dead game

In reading about the Glen Imaal terriers of Ireland, I repeatedly came across the description of 'dead game' in telling about their hunting skills. My grandfather used to use this same phrase to describe his springer spaniel hunting dogs. My sister says she always assumed it meant the dogs would hunt the game until one of the other was dead. Any hints?

Is there anything that indicates that it doesn't just mean "game that is dead rather than alive or wounded"? That seems to be what is meant by all the Google hits I looked at ("hunting dogs" "dead game").