Josephus could have theoretically witnessed the execution of whatever "James" is being referenced in Antiquities 20, but he doesn't say that he did, and he always talks about what he personally witnessed elsewhere.

"So is it as powerful as its blurbs declare?  Well, actually, no.  On the whole it is confused, lopsided and, in places, laughably amateurish.  If this is the best "mythicism" can produce then it's small wonder the academy remains singularly unimpressed."

Its under the part about the author, third or second paragraph of your link. Lol its okay dude, I like to jump around when I'm reading articles too.

The book probably isn't a good source of information but you could do some digging yourself.