Asbestos is a mineral found in nature. As such, it can be detected in all sorts of things from nature. Particularly vermiculite, and talcum powder. Bananas and Potatoes are also radioactive. None of this necessarily a prima facie health concern.
This is misleading. Asbestos is fiberous, but when locked into a brittle material, the fibers of asbestos that are released when it is broken up will be of microscopic length. So, when asbestos is found in products like plaster, concrete and tile, it will not appear to have fibers.
Asbestos was often used as a filler in plaster (so was horse hair). That appears to be plaster. It is also often found in trace amounts in old plaster, as asbestos in mineral form is often found in mined gypsum. Nowadays, the asbestos content of plaster (and talcum powder and vermiculite) is generally just about zero, since the gypsum mines that contain the most asbestos are pretty much abandoned, but it still crops up from time to time. The catch here is that if you look for asbestos, you WILL find it. Being that you live in an urban area near well traveled streets, asbestos will be found in the air that you breathe (and therefore in the dust that settles on surfaces in your home), as it is still often used in brake linings. In some ways it is like finding mold. It is everywhere.
In any case, that does not appear to be a solid asbestos product. If that were the case, you might want to take special precautions.