How could they have trained on books that they didn't buy or source from libraries?

I'm afraid, the companies in question, have been more than happy to ingest pirated material.

Game copies don't usually include their source code.

Older games tend to have their source code leaked [0], and cracks generally are designed from reverse engineering, revealing parts of how systems work.

And the forefront models have intentionally been trained on quite a bit of reverse-engineering.

[0] https://en.wikipedia.org/wiki/List_of_commercial_video_games...