Dogs with limited mobility for any reason, including age, can still enjoy a good game as long as it takes their abilities into account, rather than any disabilities. If short walks (or no walks at all) are all your dog can manage, they still have a brain that needs to be kept active.
Dogs will always have their sense of smell, so hide some treats (or a portion of their dinner) among some scrunched up old newspapers in a cardboard box and let them have a good rummage around. To start with leave the treats loose, but as your dog gets more experienced, try wrapping them up in the paper so they have to tear through. If your dog has difficulty, use some smelly cheese, or some chicken you've left in the fridge for a week so they don't have to work so hard.
A shallow box works well for dogs who may want to play when lying down, for smaller dogs, get a big box and cut a hole so they can get right in. Hiding food in your dog's blanket can do just as well, but use dry biscuits so they don't go mouldy if they aren't found. Hide their favourite toy if you have to watch their weight.
As your dog gets better, make the game harder - less treats, more newspaper, treats with barely any smell, more cardboard boxes nested together, stuff an old cardboard toilet roll with his dinner or a chew toy or treat or drape a towel over the top of the box so your dog has to work out how to get it off to start the game. Put a box upside down, or with the flaps closed so your dog has to really think how to get into the box. Even if they chew their way in, they've still had to work it out.
Float a treat or a toy that your dog loves in a bowl of water and let him work out how to fish it out - then let one sink and have him learn to dip their nose in. This is best done outside, but some plastic sheeting and newspaper or old towels can make it an indoor game.
You can also create tasty ice-cubes by putting a small piece of hot dog sausage, tuna, or anything else your dog likes into ice-cube trays, covering with water and freezing. These can then be scattered around the garden, left in a bowl, or again, dropped into water so your dog can learn to dip his nose in to fetch them. Start with shallow water, but most dogs learn quite quickly to blow bubbles while their noses are under water.