So wait... because you buy/rent things at other places than a store, a store is not a place where money is exchanged for goods and services ?
I don't quite follow your logic here. You're claiming that because a Rectangle isn't a square, then obviously a square isn't a rectangle...
Depends, eBay themselves don't really sell anything. They offer brokerage services for auctions. They are a auction house. Are they different eBay stores stores though ? Of course they are. They aren't operated by eBay though.
You limit your vision of what a store is. A store can have very different models of stocking up on goods. And essentially, if you go right down to it, the App Store does "buy" goods and "stock" them. They just pay the "distributor" after a sale has occurred instead of before.
You limit your definition of a store to a retail store. What you're describing is retailing.