I don't think this is correct. Both could be solved by determining the perfect move for each board arrangement, leading to a very simple, but very data-heavy solution (see: https://en.wikipedia.org/wiki/Shannon_number - number of chess positions somewhere below 2^155 - and also need to track for each position whether can empassant for each pawn like X-FEN does, and http://tromp.github.io/go/legal.html - number of Go positions for 19x19 board ~2.081681994 * 10^170, though other-sized boards would each need their own set of solutions). In addition, both Chess and Go engines have beaten masters:
https://en.wikipedia.org/wiki/Human%E2%80%93computer_chess_m...
http://www.wired.com/2016/03/googles-ai-wins-fifth-final-gam...
You could be correct about the human brain being incapable of storing all of the Chess or Go solutions. While the brain could perhaps memorize enough strategies and board positions to substitute, the theoretical maximum of 2.5 PB may not be enough to hold all board positions and metadata.
http://www.scientificamerican.com/article/what-is-the-memory...