As the other commenter has noted, there were a lot of actualities of local fire brigades heading out to fight a fire in the early days of cinema. Part of it was the excitement of the action. When I was a kid, every evening local news broadcast was heralded by a promise of footage of a major fire, so that impulse did not go away. Another impulse was local pride. I have little doubt that the short of, say, the Cleveland fire department rushing to action played frequently in Cleveland.
As for this one, it's much of a muchness. True, we don't see the firehouse doors open, but we still see the horses galloping, the boilers steaming, and kids running along to accompany the wagons.
As a New York City native, I'd like to tell you where this one was shot, but other tha it being typical commercial street, there are no landmarks to identify it, There are still blocks like that in Manhattan, like 22nd Street between 5th and 6th Avenue; however, in 1903, it could have been any of a thousand.