Instead, we permit that the game of chess really does exist in the world and therefore the game of chess is chess itself. A game of chess is itself chess. Crucially then, a game of general intelligence is itself general intelligence. And since general intelligence is generally intelligent, it would be capable of generally intelligent things.
If I understand(which honestly I don't) I read your argument as
A game of chess is chess itself
This can be extrapolated to "A game of X, is itself, X"
Therefore a game of general intelligence is itself general intelligence.
I believe that in the third step you may be conflating the name of the game with it's properties. Chess doesn't possess any particular expression of the idea "skills needed to beat chess", except for the fact that if you were to apply those skills to it, you would win that game of chess(assuming the game is winnable, of course).
I believe that the correct interpretation of the statement in step three would be "(The 'General Intelligence') is itself (the Game of General Intelligence).
If I understand(which honestly I don't) I read your argument as
I believe that in the third step you may be conflating the name of the game with it's properties. Chess doesn't possess any particular expression of the idea "skills needed to beat chess", except for the fact that if you were to apply those skills to it, you would win that game of chess(assuming the game is winnable, of course).
I believe that the correct interpretation of the statement in step three would be "(The 'General Intelligence') is itself (the Game of General Intelligence).
Sorry if I have misinterpreted your statements.