I don't know if those who are well past retirement would find golf so appealling unless they are in great physical shape. It may not look it, but to be a great golfer you really have to be at the top physically. How else can you make a ball go hundreds of yards. At a certain age, most people should probably stick to bocce ball.
I don't know if it is the best sport old people can play, it is certainly the most relaxing. They aren't all that good though, the senior PGA may give you a distorted idea of how good old people are at this game.
Tennis can be a good game as well for old people, though it is harder to play physically.
I always see old aged people playing gold, and for some reason I see old women playing golf more then old men. It's definately a sport that can be played in old age because it doesn't require must physical activity.
Golf is a good sport for older people because it's more slowly paced and you don't have to walk that much if you don't want to. On the other hand, it can be a good healthy activity for older people with all the walking you can do if you don't rent a power cart and you carry your own clubs. Although I haven't seen that in a while.
Hehehe, you might feel differently when you hit 60 yourself.
I think most retirees can play golf well into their 70s if they're not hampered by some serious health concerns. It's not that physically taxing, especially if you travel by golf cart or play the par 3 maybe. There are definitely some old duffers on the course from time to time who should hang up their clubs.
Other sports for older people? I think they should continue doing whatever sport they played when they were younger as long as they still can do it without physical risk. If they aren't capable, then they're going to have to reach the point where they give it up for something a little more sedentary like bocce, horseshoes, and all the old standbys (poker too ).