A store is the wrong analogy for the point you're trying to make. A store has the dimension of locality, which means that a store that duplicates another one exactly but is in a different location can still propser. (Starbuck's, McDonald's, etc.)
If you're selling worse quality products at a higher price than Wal-mart, then yes, it is silly to start a store right next door. You will probably lose money, like most startups based on bad ideas.