It doesn't seem to be breaking any laws but it's certainly unfair and anti-competitive. This time Amazon is asking its customers to use its Price Check shopping app on products in retail stores and then turn around and buy the same items from Amazon and receive perks in the forms of discounts and credits. Of course people have the right to shop wherever they want, but asking people to troll stores and then robbing those stores from potential sales seems a bit sleazy
Amazon could argue that people could browse its web site just the same and then shop elsewhere but that is hardly a fair comparison. Amazon's costs are much lower and it's not saddled with collecting sales taxes in many states. A brick and mortar store has a multitude of cost factors to bear in order to accommodate its shoppers. Amazon has only a fraction of such costs in comparison because of its online nature.
Is Amazon's tactic of using the physical stores as showrooms fair? It doesn't seem to me. And if one insists on shopping online, why not use eBay instead? It has more selections, better prices, supports small business much more widely and probably pulls fewer dirty tricks.