It may seem like Walmart is following the footsteps of Sears, but they are not out of the game yet. They need to face the innovator's dilemma head on and do it quickly because the broader issue is their e-commerce growth rate is declining instead of accelerating and the way people shop is fundamentally changing. They need to be dominant in e-commerce to be a dominant retailer in the future.
Walmart is better positioned than anyone to take on Amazon online. Their massive distribution footprint is a huge asset they are not leveraging. They need to morph into a logistics company and announce an all-encompassing same-day delivery service. They also need to completely re-haul their web/mobile UX.
I would gladly buy from Walmart. Amazon is just a lot easier right now. In the end, Amazon is not all that differentiated and if Walmart had some strong technological leadership, they could certainly close the e-commerce gap.