Is the boldfaced participial construction used properly? If not, why?
The car crashed into the building, the driver dying instantly.
It's correct. I might say, "The car crashed into the building, with the driver dying instantly." And instead of "dying instantly," you could say "being killed instantly." The way you wrote it, without the preposition "with," the sentence sounds technically correct but formal and almost literary/poetic to my ears.
I did a Google search for the phrase "the driver dying instantly" (in quotes), and the first two results I found were the following:
On Saturday at 4pm on the R21 between the Olifantsfontein and Bapsfontein turn-off, two motorcycles sideswiped each other and one collided with a steel barrier with the driver dying instantly on scene.
...away from a fatal head-on collision with a Volkswagen Golf with the driver dying instantly and two passengers passing away later in the hospital.
But then there are two more results after that that don't use the word "with":
He finds an auto rikshaw that goes off road and meets with an accident, the driver dying instantly.
The truck exploded, the vehicle engulfed into a fireball, the driver dying instantly as the flames consumed them and the half eaten dead bodies in the back of the truck.
So, this very unscientific survey confirms my feeling that including "with" sounds natural, but certainly it's grammatically correct the way you have it written.