Does he provide any context for that remark? Like, what he means by "most ancient societies." Any geographical area?

I can't say it never happened anywhere ever. But I agree with you that I it's safe to say that it wasn't the norm for "most ancient societies" and certainly not "after only a few years." My source would be the written and archeological evidence we have for long reigns in societies all over the world.

As for where he could have gotten that idea. The whole concept of the sacrifice of the sacred king was brought up in Frazer's the Golden Bough. The Golden Bough was certainly a huge inspiration to a lot of writers and artists. But it isn't taken seriously as a historical source. And he isn't claiming to be creating a history but examining what he believes is a pan-European and perhaps universal mythology. Although it isn't taken seriously as a true study of mythology either. But, as I said, it did influence a lot of literary sources and it's possible Greene (or 50 Cent, I guess) read it somewhere because of that.

The Golden Bough is public domain. So you can take a look at this yourself: http://www.sacred-texts.com/pag/frazer/gb02403.htm

There are certainly a lot of myths and stories that involve a ruler or a member of the royal family dying. But little to suggest this was reflective of a ritual sacrifice of kings. As context, there is a thread of the study of mythology that believes all myths are stories that represent a specific ritual a society performed but it's not highly regarded to that extreme anymore. There is an obvious connection between ritual and myth but no reason to believe one is a literal recreation of the other. So, just because kings died in myths doesn't mean they had to kill a king to perform some ritual.

There have been bodies found in Ireland that some have insisted were the remains of sacrificed kings. There was a documentary about it. Ghosts of Murdered Kings. Interesting suggestion but I remain skeptical. And even then they don't suggest this was a common thing that occurred every few years (and there isn't the archeological evidence to support that idea) but done because he was blamed for bad harvests or other "bad omens." Again, I remain skeptical. He could have got the idea from this or an article he read about it. And embellished.

ETA: I should be more clear when I discuss Frazer's work. It is certainly historically true that cultures all over the world believed their rulers had some divine or sacred connection. Some believed they were literally a god. I am not dismissing the fact that many cultures believed their kings were sacred. Just that there is little evidence that they were regularly ritually killed.