The whole radar unit and lots of the intelligence in it comes prepackaged from Bosch. So yes, plenty of high-end cars do this.
I work on these units as a hardware engineer for a manufacturer. They are very clever bits of kit and a lot better than the other offerings on the market.
And to support your comment - yes, this isn't exclusive to Tesla by any means!
I think Mercedes has a feature called PRE-SAFE Brake which does something like this.
I drive one (C350e), and indeed it monitors traffic and brakes when another car in front does too. Now the question is: "does it really matter that the car can see through the car in front"? Because if the car is self-driving it will keep such a distance that it should be able to brake & stop safely if something happens in front of it. Meaning: the Tesla should still be able to come to a safe stop even if it only detected the nearest car was braking - just because of a -say 2 second- distance between the cars.