A lot of people don't realize that chess players peak around the same age as athletes do. Carlsen was at peak dominance in his mid-20s. Kasparov peaked later, at 36 years old, but still, it wasn't at age 50 or 60.

Chess requires you to be really sharp. Experience increases with age, but there's some cross-over point at which the decline in calculating speed is more important than increasing experience. Heck, I'm measurably better at chess tactics in the morning after a good night's sleep than in the evening after work.