Yes you can... to a certain extent.ding ding ding. I agree.
The store is called the App Store. You can't copy someones store name.
Two stores can be named the same if the name is generic in nature.
Apple didn't create the word "App Store". This has been proven in many threads about this very topic.
They popularized it and then went so far as to even give it generic meaning.
Steve did that himself. Now he's trying to lay claim to it after the fact.
Will he win... who knows.
But nothing is as black and white as many claim to believe it is.
Trademark law is complicated.