Cats kill their prey by delivering a neck bite that severs the spinal cord. To do this, they must temporarily release the prey to get at the nape of the neck, but when they do so, they risk the prey escaping or counterattacking. Small animals will defend themselves if they get the chance. Mice, rats, and other rodents can deliver a vicious bite, and birds can peck. A cat has a very short muzzle, and to get close enough to apply the neck bite, she risks injury to her eyes and face from the prey.
A cat will “play” with her prey to tire it out in order to reduce the risk of injury to herself, but she is not actually playing in the human sense. She is simply doing the job that her instincts tell her she must do in order not to starve, and protecting herself in the process. If the prey is lively, the cat could suffer a serious bite that might become infected and lead to death. Only when the prey is sufficiently tired and dazed is the cat able to make the kill.