I don't like NASCAR much, I prefer the speed, power, and handling of the cars in the CART series. I'll get to your question in a bit, don't worry. Most people don't know how physically fit the drivers in the CART series have to be. Their heart rate averages 160 bpm for the duration of the 2-3 hour race (the drivers are constantly straining, and because of the g forces, it's harder for the heart to pump blood to the body's extremities), they sweat off a few pounds during the race, and they have to be strong enough to counteract the Gs and have enough stamina to do so for the whole race. So auto racing at the highest level requires the driver to be physically fit and of course to be quick mentally.
But is auto racing a sport? I can't find a good definition of 'sport' so I get to make up my own answer
I'd say that auto racing is a sport. It has a physical and mental element and requires a lot of talent.
Mike