Do you know what the "General" in "Artificial General Intelligence" means? It specifically means that the AGI adapts to novel domains that it hasn't been trained on - its training generalizes to real world problems.

That doesn't mean it has to be extraordinary at these things. But to be AGI, it has to have some level of competency when used on problems outside its training set. In particular, it the LLMs were to install a known chess engine and run that to get the moves when asked to play chess, that would qualify for more AGI-like behavior. But really, chess is such a simplistic game that they should be able to do decently well at it even without even needing that. At the very least, they should be able to consistently play without making illegal moves - something that many 7-year olds manage quite well.