You don't have to run to be in shape. I know most of those are "individual sports," but I have an uncle and aunt who play tennis together daily. They are in good shape and it's one thing they enjoy doing together. I play volleyball with older guys in my ward (one is over 65). It's fairly competitive, fun, and good your heart rate up.
The wear and tear from most team sports a la basketball and football would keep most 60 year olds at home though.