As you note, transformer (and indeed, most ML) models do create a "world model". They're useful for 'specific' intelligence tasks.
The problem for general tasks lies in their inability to create specific models. To stick with the board game example: The model can't handle differently shaped boards, or changes to the rules.
I could ask a human and a chess-trained AI system to, for a given chess board state and piece, what places that piece can move to. Both have their model of chess.
But if I then ask, "With the rule change that the pawn can always move two spaces", the AI cannot update their model. Where for the human this would be trivial. The human can substitue in new logic rules, the AI cannot.
And that is very core of what's required for generalized logic and "thinking" in the way most tasks require it. What's so troublesome about current generative AI is that it's trained to be extremely general (within the domain of text generation), so their internal models aren't all that good.
Ask an LLM the chess problem above and you might even get a good answer out, but it doesn't generalize to all such chess problems, especially not more complex ones.