The first question is, is this offering a delight for the shopper? The obvious answer is yes. Especially for the prime shopper, who loves selection and convenience, one day delivery is a big positive.
The second question is, should other retailers go after this feature. The answer is not easy. Amazon's DNA is about faster delivery and it will keep upping the ante there. But that is not the DNA of every other retailer in town. And one day delivery is expensive.
I personally don't see much difference between a one day delivery and a two day delivery option -- I would rather choose a delivery option when I will be at my apartment or choose a click-n-collect method, which is tough for Amazon to provide. I think retailers should see what matters more to their shopper and innovate there, instead of going after this new challenge. Do no knee-jerk announcements to match Amazon here. Having said that, they all need to invest in delivery to keep pace with the growing expectations and strategic actions on the same would have slow but long term implication.