Unlikely. Winco is by far the cheapest grocery store chain in the area, and no Walmart is far from a Winco. In other areas, this would absolutely be true but in Portland the impact is likely to negligible if at all. I’d honestly assume, like the others have said poor performance is the reason for closing not theft.
You obviously can't ship regular groceries through traditional carriers, and grocery delivery relies on local stores being able to fulfill.
Even if they kept the stores open as a form of a delivery and pickup hub, it's still disadvantages low income individuals or families that do not use technology heavily enough to be able to use the app, or the delivery fees/tip structure could make the cost prohibitive for low income folks.