But does one's brain really need significantly more oxygen when playing grandmaster-level chess?!
I suspect NOT.
Playing grandmaster-level chess certainly requires intense concentration and the heavy burdening of certain cognitive abilities - one could certainly see evidence of this in a brain scan taken during a match. And I'm sure that the tournament participants are very stressed out, psychologically. This might result in heavier breathing, etc. But that's physiological!
But even when simply sitting and reading a comic book, the brain is still performing lots of high-level tasks. It's still processing lots of information. I sincerely doubt that the O2 consumption is noticeably lower then.
Regards,