Looking at Transformer model architecture and their training schemes to understand how they think misses the point. You wouldn't gain insight into how Doom game works by just looking at schematics of an x86 processor.

These systems are Turing complete and they can execute any computation. To see what they actually execute requires looking at what happens in memory while Doom runs, in the activations when the Transformer model executes.

At this time we don't have good tools to extract the actual algorithms and submodels these LLMs execute, but there are reasons to believe there are better algorithms learned in there for example for reinforcement learning than what we have ever been able to engineer.

See for example my research: https://github.com/keskival/king-algorithm-manifesto#readme