In your hypotheticals, if Ford controlled all dealerships then refusing to sell GM would be anti-competitive.
If Apple controlled all physical stores where computers are sold, it would be anti-competitive to refuse to sell Microsoft.
Amazon directly competes with Chromecast and is dominant on-line retailer in US so they do have have the power to alter dynamics of Chromecast vs. Fire TV competition. That's what makes that anti-competitive.
Notice that a big part of amazon.com value is being a platform to others to sell their stuff. I certainly bought stuff via amazon.com that was not sold by Amazon, merely distributed by them.
To go against that platform "neutratlity" (if you will) and refuse even 3rd parties to sell a very specific product, while allowing thousands more, is pretty damning evidence that it's straight up, anti-competitive leverage of their position in one area to gain advantage in another area while negatively affecting customers.
what? That's complete nonsense.
If I want to bring something to market, I can't just force my competitor to sell it in their stores. "Dan's Cars" could start up and force Ford to sell their cars in the Ford stores - crazy.
That's not how this works. If "Dan" expects to sell cars, then he has to do that himself, not rely on, or expect his competitors to do that for him.
How Dan's competitors sell their cars is frankly none of Dan's business.
1. Market share matters, for what should be obvious reasons. Amazon is, in that regard, a far cry from your sole proprietorship fruit stand.
2. Amazon is much closer to Walmart than it is to Apple or Ford; Amazon didn't do retail to support their product line, they rolled out a product line once they dominated in retail.
3. Sure, consumers can go order a Chromecast from somewhere else; just like how users could always download Netscape on Windows. That didn't stop antitrust claims from being brought against Microsoft for their practice of tying, because they were fundamentally abusing a dominant position in one market to assure their dominance in others despite weaker product offerings. And here we are, with everyone subscribed to Prime for the free shipping, and getting an unasked-for set of streaming services bundled with. Which aren't compatible with Chromecast. Which Amazon uses to justify banning Chromecast from its store. It makes the tying of MS years past look amateurish by comparison.
Analogies are limited but to play along, it's as if you own the largest supermarket in a place that only has 3 orchards (assume you're isolated from the rest of the world), and you own one of those orchards, and ONLY sell fruit from your orchard while refusing to sell fruit from the other 2 orchards.
Those other two sell directly to the customer (and to small grocers) so they still survive. But they miss out on the customers that come to the supermarket and might have otherwise bought fruit from those other 2 orchards.
If I go to the trouble of building a store (bricks n mortar or online) then I'm going to sell what I want to sell.
I built the fruit store, NO, I don't want to sell live Aardvarks from my store, and it's preposterous that you think you can force me to do that.
I built a store to sell my stuff and make money, after all.
This is such an interesting topic.
If I open a fresh-fruit stand and refuse to sell the Chromecast and I being anti-competitive? How about if I grow my own fresh-fruit and refuse to sell yours in my stand?
The whole reason for me to spend money running my own store it to sell my stuff, not yours.
What about if Apple open an "Apple Store" and refuse to sell Microsoft products? Ford dealership refusing to sell GM?
It's Amazon's store, they can sell whatever they want, or not sell whatever they want. If you don't like it, shop elsewhere.