A normal chess match last about 4 hours. If we divide proportionally the energy of the day, that will be about 400Wh. I remember a factoid that says that the brain consume the 20% of the energy of the body at rest (less % while running) (more % while thinking?), so if we cut the unnecessary stuff [0] that will be 80Wh, i.e. 10 batteries. Probably the phone is more efficient.
So 10 batteries... how long do you think the engine could last on one battery? Then we multiply that number by 10 and see if it's less than 4 hours... hmmm
[0] Don't try this at home.