Groceteria.com

By any chance is this a former A&P Centennial store?

https://www.google.com/maps/place/Ocean ... gIgARICCAI

That building does look fairly A&P-like! But given the specifics, I'm going to have to say this wasn't one...

* The building is easily 50,000 square feet in footprint, and doesn't bear any traces of being expanded. That's far in excess of what a 1950s-1970s supermarket would be.
* The ends of the centennial roof have a vertical cutoff. All the genuine A&P centennials I've seen had a slanted cutoff.
* The entire shopping centre has matching architecture...which tells me it was built by a developer going for a pseudo-colonial vibe.
* I checked Historic Aerials, and the site of the store was wooded wilderness in 1974. A&P had already stopped building centennial stores by that point.

It could have still been a supermarket. The entrance looks supermarkety.

There is what looks like a (fairly) new Market Basket basically next door (with a Marshalls) - so perhaps that was their older store at one point?

This was a Purity Supreme (1988-1995) and Stop & Shop (1995-1998). The Stop & Shop closed when they opened a store at the Myles Standish Plaza a couple miles down the road.

Here's a photo in the Purity Supreme days: