If you meant they have been around that long, sure, they have, but a stromatolite is not a living organism by most (if not all?) definitions. It is a layered sedimentary formation. It is about as much an organism as an ant heap without ants is an organism.
And I'm pretty sure that none of the individual organisms that create stromatolites are even close to a 100 years old, never mind a billion years old.
But less philosophically, when people refer to “living fossils”, they generally mean that the organisms haven’t changed much in form or physiology in a long time. There’s no reason to believe that they aren’t subject to the same pressure to adapt to changing conditions via natural selection, but those adaptations aren’t readily visible.
Good question, I looked around a bit for this, it seems the life of a single celled organism is taken to be from division to the next division, but really this is a bit odd, because nothing died there. Clearly age for such organisms is not a well defined concept.
The point they are making is that stromatolites have existed for billions of years according to the fossil records.