From skimming the conversation it seems to mostly revolve around LLMs (transformer models) which is probably not going to be the way we obtain AGI to begin with, frankly it is too simple to be AGI, but the reason why there's so much hype is because it is simple to begin with so really I don't know.
As for abstract reasoning, if you look at ARC-2 it is barely capable though at least some progress has been made with the ARC-1 benchmark.
The Turing Test is whether it can fool a human into thinking it is talking to another human not an intelligent machine. And ironically this is becoming less true over time as people become more used to spotting the tendencies LLMs have with writing such as its frequent use of dashes or "it's not just X it is Y" type of statements.