If that is all you have then the next chess move will be random (or whatever token is more likely in isolation), or the stock prediction will be the same.

For the chess example to work you need the current board state in the context or the move history. How an LLM performs will depend on what it has learned across the transformer layers and in the residual stream, as well as how much chess data it has been trained on. -- NN models like Leela and Stockfish have been trained on thousands/millions of games and have a game-specific state space representation.

The stock prediction example is similar, but doesn't have a consistent state space in which to make that prediction. It will need information in its context (current news articles, stock history of all stocks, etc.) in order to be able to make a prediction. Its performance will depend on whether it has been able to learn factors that make it possible to make accurate predictions.