Amazon is simply a store for majority of the people who shop there.
If Google banned Amazon from search results you would probably be outraged.
The news article says that they're banning video streaming devices that don't support Amazon Video. So if that's true, it's not that they're banning competitors, but that they're forcing streaming devices sold on Amazon to support Amazon Video in addition to whatever else they support.
I don't know what the primary motivation is, but I could genuinely see some customers being confused. Imagine you're a customer that's just signed up for Prime. You don't have a TV stick to watch it on, so you shop around the store and find a streaming device that's highly reviewed. You buy it and plug it in, only to find that Amazon Video does not work on it, or works poorly. This is plausible; this kind of thing happens, especially with unsophisticated, less computer savvy buyers (the kind of people who think the Google search box is the Internet). I could easily see my parents making this kind of mistake.
Whether that's the primary motivation, I wouldn't know. It seems like you could also deal with that problem by changing the way the product is displayed, for people who have Prime Video, and show a big warning like "This product does not support Prime Video" on the side so they can't overlook that fact when buying it. (Though this could lead to other complications - I could imagine there being weird legal or anti-competitive issues with making claims like that about competitors' products in a way that they can't control, that's not part of the product description. Banning them might be the simplest way.)
The only reason the devices don't support Amazon Video is because Amazon has chosen not to build apps that support those devices.
This is a problem entirely of Amazon's making. And I don't understand it. No one makes money on the devices, they make money on the subscriptions. It's in their best interests to be on as many devices as possible.