Earlier quoted context omitted.
There are several activities right now that people keep doing despite machines being better suited: martial arts (and more in point, HEMA[1]), handicrafts, several Olympic sports. Why would anyone attempt to run a marathon under two hours, when any car can do it in 30 minutes? I think the answer lies less in "I will be the absolute best", and more along the lines of "I will do it better than anyone before me". And so…
It does feel like there's a difference–maybe Go and Chess are just so much closer to what defines humanity than any physical sports?
I suspect this stems from the fact that each game imposes its own set of artificial restrictions. Of course you don't ride a horse in a footrace; that's not the game. Just as you don't confer with your team of experts in a Go game. A game is only given meaning by the artificial restrictions it defines.
Within the bounds of the rules of the footrace, the game is still competitive for humans; currently this is somewhat tautologically so. (Though I think we will have a similar conversation to this when human cyborgs can out-compete unmodified humans [1]). The fact that there are things faster than a human outside of the bounds of the game is irrelevant.
In Go, within the bounds of the rules of the game, humanity cannot compete at the highest level any more. I see that as a big difference.
[1]: http://www.popsci.com/technology/article/2009-11/seriously-d...