Margins in this type of enterprise are extremely thin. Only works in small areas with extreme population density. We had WebVan, an internet grocery, in our city in the late '90's that quickly went belly up. I worked at a pharmacy at the time, and our wholesale pharmaceutical distributor, McKesson, had an almost identical operating model. Same delivery vehicles, same tote bins, same type of handling machinery in their warehouses.
Margins for pharmaceuticals are far better than groceries, and even McKesson was refining their delivery system, selling off their private fleet and switching to contracted owner-operators for deliveries.
It was just a tragedy to lose the grocery service. Though the prices were on the the high side, sitting down at a computer and precisely planning your menus for an entire week or two saves a bundle in the long run. In retrospect, that very behaviour may have contributed to their downfall.
The one thing that these guys may have going for them is their point of purchase model. It lends itself to impulse buying, and that may make the difference in success and failure for them.