The chess player says he isn't good at fixing watches. The friend is surprised because he is good at playing chess. The friend thinks that both amount to solving problems. If the chess player can solve difficult chess problems, why can't he solve the problem of fixing a watch?
The chess player is explaining the difference between two skills. The skill of watch repair and the skill of chess playing are not the same.
The chess player says "But that's the thing... if one of your watches breaks, there's only one way to fix it."
In watch repair, there is only one correct solution. In chess playing, there is more than one way to solve the problem, and creative thought is rewarded.
In fixing a watch, creativity does not help you. You have to know which gear goes where.
P.S. The topic reminds me of a great book, "Zen and the Art of Motorcycle Maintenance: An Inquiry into Values," in which the author, Robert Pirsig, makes interesting connections between machinery repair and the big questions of life.