A large language model trained on Othello games will actually build a "board representation" inside its neural network: https://thegradient.pub/othello/. This was confirmed by editing the board representation inside the neural net, "tricking" it into "believing" the board was in a different state. At this point, the LLM started making legal moves based on the edited position. If the LLM is actually building a data structure describing the board state, then it's hard to claim it's just acting as a parrot.
The raw version of GPT apparently achieves an Elo score of 1800 at chess: https://twitter.com/GrantSlatton/status/1703913578036904431. This is worse than a good dedicated chess engine, but almost certainly better than I could do!
And every day, I see Copilot occasionally perform non-trivial completions that require "in-context learning" of complicated things that exist only in my source code. Sure, it crashes and burns regularly, too, but I've seen a lot of cases where it could only have figured out the code it did by carefully combining information available in the file.
So I believe that LLMs can actually achieve surprisingly large amounts of understanding, particularly ChatGPT 4 and (on a good day) CoPilot. But the frustrating thing is that they're inconsistent, and the current RLHF process apparently impairs their ability to correctly estimate accuracy. When they make mistakes, they're effectively "blind" to those mistakes, to a shocking degree.