I really hope Instacart and Postmates can compete with them! I see different use case for all of them. My first choice for groceries that i need the same day would be Instacart, i also love the on-demand food from great restaurants and the ability to get a few grocery items within the hour by Postmates and Google Shopping Express looks like a good Amazon alternative.
Which makes sense - mostly non-perishables shelf-able items. At first, the lack of groceries made me wonder if it was useful at all, but being able to find e.g. 2 gallon-sized jugs of distilled vinegar awaiting at my doorstep is quite nice (local stores often just don't carry the stuff).
Also Instacart has TJ's. That one store is a winner all by itself.