That kinda defeats the purpose. Of course you can use AlphaGo, but the question here is – can a generative AI teach itself to play chess (and do a million other similar generic tasks) when given no specific training for it.
This has bigger ramifications too: if GPT4 learns how to use RPCs effectively, it can do accurate complex mathematical computations and simulations, do IoT/home automation tasks, and even control heavy machinery.
Isn't it very likely chess games were part of the training data? If so, chess sequences seem like an amazing matched filter of sorts. It doesn't seem surprising that it can guess a next move.
Is it teaching itself anything here? Is the model being updated in any way? Or are you talking more generally, looking into the future sort of statement?