No, I don't consider NASCAR a sport. To me a sport is defined as two or more teams going head to head with a single minded goal to work together and achieve victory. A ball, puck, or other inanimate object must be involved in scoring points as well.
To that extent some would argue that racers have teams and work together or whatever, but...no....they don't count in my book. At the end of the day it's every man for himself. I also don't count gymnastics as a sport. It's extremely athletic, not something I could do personally, but it's an activity or event in my opinion and not a sport since it involves less teamwork and more individual achievement. I once got in a debate with an ex gf over the qualifications of gymnastics as a sport and she told me to get out of the house