Game theory: reconstruct the rules by watching a chess game

Imagine You don't know chess and You watch an ongoing game. You watch move 5 to 40. You watch very carefully and You try to reconstruct all the rules of the game.

Much more complex is chess. It is beyond the power of today's computer to create a list of every move until the end of the game. Only in a critical situation, it is possible to say that a certain move will create a lose situation in 5 moves for example.

In the view of the game theory is chess also a simple game. All rules are known and every player has full information about the advance of the game.

Imagine: You don't know chess rules

Imagine You don't know chess and You watch an ongoing game. You watch move 5 to 40. You watch very carefully and You try to reconstruct all the rules of the game.

Ends a chess game when one player has no figure left, or when both towers are out of the game, or when the king is captured? You can only assume some rules by watching an ongoing game.