The reason is it is competition. Amazon makes games, you can't make games. If you want to do any sort of outside development then you have to ask permission, they can shut you down with or without explanation and they currently have a blanket ban on games. Or game engines, or anything related to games.
This includes starting a blog just to talk about game mechanics or the like.
Technically you aren't actually banned from making a game. It's just that you can't ever publish it, show it to anyone, or talk about it.
Of course if you apply you will get told it is no problem to do outside development.
Is this showing up in the contract you have to sign?
In places with more diversity in tech employment (say, Silicon Valley) you will find less bullshit contracts like these, since there is more competitive pressure between employers. In Seattle it's Giant BigCorp A or Giant BigCorp B, with a smattering of smaller tech companies (or satellite offices, see: Google).
In the contracts I've seen with these kinds of terms, usually there's a way to disclaim things you've already worked on, such that those specific items are excluded from the contract. So, for example, if you were working on some open source lib already, you can enumerate it in the contract and that won't be covered. Of course, this still greatly limits your freedom to start new things while employed.
It sucks. It's a blight on our industry.
So you sign a non-compete, but if you ask you get told that things like games or open source contribution are fine.
Then you come in and you find out that internal policy is that you need approval for everything. That's not that unreasonable, and they are usually not too slow. for most things they don't have a blanket ban.
THen you don't quit immediately because you don't want to hand back your signing bonus, but once you it that one year mark it becomes an option and many people do quit at that point.
In some cases it really does make sense, where you have privileged knowledge by working at the company and directly competing publicly using that unpublished insider knowledge is pretty obviously a bad idea. A lot of companies actually have pretty legitimate review boards that will quickly approve anything not directly competing for public release.
On the other extreme, some companies basically refuse to approve anything for external release: my father as an EE at IBM wasn't allowed to release templates for making labels for homebrew beer bottles. An ex-IBMer on my current team worked on a relatively small piece of software that would have been great to open source (and really not competing with any of IBMs initiatives) but IBM wouldn't allow it, nor did they want the project to be continued or used in any meaningful way.
I am so never working there.