chess is not just a rigorous set of rules, it is rules as foundation with layers of strategy on top. and so is, for example, scientific methodology or chemical interactions or virtually everything else under-the-sun that comprises human knowledge
knowledge for chess is derived from memorizing strategies that have been well-defined for decades paired with in-game reasoning processes. this is not at all different from any other body of knowledge. Noble gases, laws of thermodynamics, organic chemistry just to name a few - these are all 'strategies' that define observed phenomena, analytical frameworks that trace a logical, rational set of interactions and which can predict the next
for an AGI, all of this should be a cakewalk, trained as it were to surpass human capability in any and every domain [0] (thus the G for 'general' and not 'N' for 'narrow' [1]). it should be a natural at everything, infinitely adaptable on-the-fly. the whole point of AGI is that it surpasses human capabilities even at our frontiers and bleeding edge (unless you're private enterprise and you've moved the goalposts for industry [2])
currently, it's only AGI-seeming if it gets benchmaxxed enough. otherwise it sucks at what it does and then is only barely competent at tasks if paired with enough skills and tests to make it more diligent at its work. this makes sense to me - for any probabilistically trained tool, even one that you post-train and fill with nothing but the best-quality evidence, the ultimate result is the lowest-common-denominator output for your sample set. there's no natural reasoning the AI does itself to make itself better at what it does - it's all human curation and categorization of sources ingested paired with RLHF post-training that we can get the mediocre-at-chess-at-best results that we see now and the benchmaxxed scores against whatever arbitrary and pre-defined measure
that's not AGI by any classical definition. that's a cool, useful, and powerful tool that makes our lives easier, much like a hammer, nail, and studs make mounting a picture frame easier than if we only had our hands alone
[0] https://ischool.syracuse.edu/types-of-ai/#:~:text=General%20...
[1] https://aiethicslab.rutgers.edu/e-floating-buttons/weak-ai-n...
[2] https://aibusiness.com/ml/what-exactly-is-artificial-general...