I believe that's the Tuned Turbo Challenge, race 2--the one at the Test Track--in Special Events. Could be wrong about it being race 2, but it's definitely in the Tuned Turbo series.
You either win that or an alright Nismo Skyline; it's random.
You win the Drag 180SX in the 3rd race (the bottom event) in the Pacific League. The Drag GT-R is a random prize car awarded at the Tuned Turbo No.1 events (you may win it at any of the 3 races).
After I posted this, I thought I'd try to get the Drag 180 to do some top-speed runs. I'm still fighting the handling, but at least it's steady on the straights! I read somewhere it turns like the Titanic, but it really moves more like plate tectonics.