why would they pay a bunch of money?

Employment is a contract. Apple broke that contract without reason from the individual.

If he resigned from another job and relocated, there are damages here that are quite easy to document.

Yes, employees are nominally "at-will", but employers don't get to just do anything they want without consequence--especially in California.

I'm surprised Apple did actually say anything beyond "We have terminated his employment. No further comment." as they're on terrible ground here.

Finally, unlike most small fry, he's not going to have any trouble finding a lawyer for this. Lawyers will happily take this obvious a case on retainer. And, he's got lots of "wokeness crusade" lawyers who will be salivating over this case.

There's a legal theory known as "promissory estoppel" or "detrimental reliance" that probably applies if Martinez's story is accurate. Apple promised him a job, he made some major life changes based on that promise, and now they've withdrawn their promise without any relevant new information or new bad conduct on Martinez's part.

Apple can claim the information was new to them, such as for example believing the book was a work of satire only to find (based on post-hire discussion with AGM) it was actually a manifesto.

They can. I'm skeptical whether that'd be true - although I guess it's really academic, because high-profile employment disputes like this are almost always settled out of court.

Under California law, because he moved for this job.