I work for Amazon. I've worked here for quite a long time, actually. I manage people, so I know how the management tools work, what information we gather on our employees, and how they're rated and ranked.

The 100% Peculiar Quiz being referred to is one of about a dozen (or so) "freebie" quizzes you can take to get a Phone Tool icon in exchange for doing nothing more than reading a Wiki Page. Most Phone Tool icons are actually pretty hard (or impossible) to get. You have to have participated in a certain product launch, or done some improbable/rare thing. So it's a fun way to get some extra icons to pad out your profile page. It also serves to help you retain the information you've read, like any quiz would.

Pretty shortly after you start, you get a "new hire orientation" e-mail with a ton of useful links in it, including the internal wiki, how to get your permissions set up, and a link to the 100% Peculiar Quiz and associated wiki page (along with about 50 other links you probably won't have time to read.) You can take the quiz or not. As your manager, I wouldn't even know unless I checked your Phone Tool page, because I don't get a notification when you complete it. (Unlike other important training like harassment, etc.)

About 75% of employees get it. As a manager, I literally couldn't care less whether you have it or not. I'm too busy making sure you can understand the codebase and use our build and deployment tools. No rating I've ever given an employee has had even the slightest thing to do with what Phone Tool icons they have. I can't even imagine a scenario where I could possibly care. We rate our employees on real things, like how effective their code reviews are, how many things they've shipped, and what their peers and partners in other organizations are saying about them.

Again, the NY Times article was strongly trying to imply that employees are forcibly quizzed, like it's some kind of brainwashing exercise. There is a quiz, but it's for funsies and nobody cares whether you take it or not.