Other companies don't propagate their corporate culture so explicitly, so it seems a little weird and cultish. But if you're a big company doing things the same way other big companies do them, you're going to get the same results that other big companies get. Amazon wants to get better results than other big companies.
When I started at Amazon, I felt like 14 was simply too many. I tried to do a Carlin-style winnowing, but darned if I could get the number below twelve without starting to lose things that the company obviously thinks are important. (They recently added two more, by the way.)
As a bonus, after a stint at Amazon, your familiarity with their leadership principles can make you very desirable to other companies. I know a number of people who were individual contributors at Amazon and were snagged by Microsoft for leadership positions, either team leads or product managers.