Exercise and play is important to all dogs, including your elderly dog.
First of all, exercise helps maintain a healthy body weight. Being overweight may lead to a number of health problems. It places excess stress on your pet's heart. Excess weight on degenerating joints can speed up the development of arthritis.
Your elderly dog's mental health may also benefit from exercise. Activity keeps oxygen and other nutrients at optimum levels in the brain. The brain is like every other organ in the body in that it requires good nutrition.
For more information, please read The Importance of Exercise in the Senior Dog.