Apple AppStore doesn't equate to a real store because there is no competition for it, and you can't run apps not from their store on your device short of jail-breaking it.
So, Android, Blackberry, WebOS, and WinMo phones aren't competition to the iPhone? Sure, the Apple App Store is the only place to (officially) get iPhone software, but you're free to buy competing phones if you are opposed to the restrictions of that store. Since Apple does not have a monopoly on smart phones, it's perfectly legal for them to decide who gets to hang out in their walled garden and who gets the boot using any arbitrary rules they might want to impose.
Here's my attempt at a bean analogy. I run a store and I sell a magic bowl. The only food you can eat out of this bowl is food from my store. I don't sell beans, so you can't eat beans out of my magic bowl. I also have a history of randomly deciding other types of food aren't allowed in my bowls, and I generally don't care what customers think about it because I think my magic bowl is way easier to use than the competition (and I'm raking in money hand over fist). There are 4 other stores on the block with their own magic bowls and they each offer different combinations of food for their bowl. You're welcome to browse all 5 stores before buying a magic bowl from any of them.
they only say it will work if it uses the easy-bake mix
Apple only says that iOS devices work with software that comes from their App store and they make the rules for their App store.
The one day you'd sell your soul for something, souls are a glut.