It would likely work better than democracy assuming the same level of compliance with how it's supposed to work (government officials not cheating, people having faith in the system, etc) since the selection criteria would likely be better than random selection and it would reduce the number of people involved in the highest levels of governance.
But it would also not be ideal since being good at go may not translate into actually doing a good job governing a country and more importantly many people suited for governing would not be good enough to win a go tournament or at least not have time for that. It would favor people who put all their effort into winning at the game rather than actually being good when it comes to actual governance.
One option is to invent a new board-game when it's time to evaluate each new official. Even here however people could get an advantage by having played similar games in the past.