Yes, I've seen reusable grocery bags in a similar material, too. The bags from Trader Joe's have the same pattern of heat-bonded dots and a tag on the inside that says "nonwoven polypropylene". Nylon, polyethylene, and polyester are also sometimes made into nonwovens of this type, but they are more costly. A dollar-store laundry bag is more likely polypropylene, like the Trader Joes bags.
I would guess that the properties of that fabric are similar to tyvek (near zero water absorption, low strength, etc.). It probably isn't waterproof, but if it seems water resistant at all you could consider it for a bivy top or a groundsheet. It might not be strong enough for a garment stuffsack, but might make a good "ditty bag".
I use a fabric similar to that (lighter, white nonwoven polypropylene) for a pillowcase/stuffsack. I made an inflatable pillow but the surface is plastic film, so I put the nonwoven pillowcase/stuffsack over it at night.