That's not true for every game, Kosuke. Look at Starcraft. Ever since Boxer joined the Korean Air Force, he hasn't been able to compete in most of the professional leagues. Some people are hanging in there like Leta and Nal_ra, but the whole scandal involving Saviour as he is out of his prime shows just how much being young really affects your abilities in that game specifically.
You reactions don't really start to show significant decline until your late 20s and early 30s, but there is still the aspect of growing and understanding a game that seems to come with those critical teen years as even the best Melee players are getting younger.
People like Daigo, Jwong, Alex Valle, and other prominent fighting game players are very rare and special for their ability to be at the top of the metagame in each installment of a Capcom fighting game. What allows them to do that, though is that the control schemes haven't changed much since the original SFII installment and a lot of the fundamentals are consistent between similar franchises. That's why you might see a lot of familiar faces going through the fighting game communities, Halo communities, but the people excelling at Halo might not do as well in a game like Counter-Strike, and in most cases, the opposite is true.
It is interesting to look at other games and find those dynasties where one player dominated for a long time. Even in our own game, Ken was years ahead, but eventually, M2K overtook him and a lot of the community also approached that level of play.
As far as games go, I think our generation will probably play games until we grow old and die, at least I know I will.
If I can **** the world at games even when I'm 50, that would be wonderful.