I believe this view can only be held by those who are ill advised of the workings of NASCAR. I contend that the NASCAR has the following qualities that most definitely qualify it as a sport:
1 - It requires physical conditioning on the part of the driver and pit crew in order to succeed.
2 - It requires an intelligent coach, the crew chief, to make critical decisions at the appropriate times in order for the team to win.
3 - It requires domain specific mental toughness and intelligence on the part of the driver and the pit crew. Just because drivers are riding in cars does not mean that they are riding in the same comfort that you do when you take a long road trip.
NASCAR vehicles are built for weight, speed and safety, not comfort. Racing seats are small, thinly padded containers for the drivers not the same luxury seats with multiple comfort adjustments that you find in all cars sold in the production environment.
NASCAR suspensions are also built for maximum grip, not maximum rider comfort. Both of these things mean that the ride you get in a NASCAR vehicle is much more similar to the ride you would get on a piece of aged construction equipment than it is to your passenger car.
Sitting in these vehicles for hours is downright uncomfortable and for the average person would cause days of back pain and exhaustion. NASCAR driver must train in order to make it through the hundreds of miles they train and race each week. NASCAR teams have coaches just like more traditional sports.
These coaches are called Crew Chiefs, they call all of the shots during the race. They decide when a car will pit, how many tires, will be changes, how much fuel will be added, and what adjustments will be made to the tire pressure and suspension. Any one of these decisions could win, or lose, a race for a team. Much like any other sport the success of the team depends on the quality of the coach. Drivers and pit crews have to be mentally equipped to deal with the situations that arise during the race in the same ways that players have to deals with situations that arise during games. In football, it is important that a player not focus too much on their previous mistakes.
For example, if a receiver fumbles a ball on one play, it is important that he forget about and be ready to play well for the next set of downs. The same is true with drivers and pit crews. If a driver gets a bad restart or a crewman takes too long to change a tire, it is important that each of them have the mental toughness to not give up on their jobs for the remainder of the race. If even one person on the race team gives up, no matter how small their responsibilities, the team can fail and the race can be lost.
After taking these facts into consideration and learning more about NASCAR it should be fairly easy to classify it as a sport. While the physical side is less pronounced than most other major sports, NASCAR still has all of the components of a sporting event.