The car is important but so is reaction time and endurance - G - forces on a neck are critical
Fast reactions is a mental ability rather than a physical, it is how fast your brain can process an action that has occured and send a response to your body. Endurance is important in chess as well as I have explained via the kasparov karpov match.
If a game where physical skill is what matters the most, is what a sport is, I still hold car racing would then be disqualified as a sport.
When we go for a prize were honor and supremacy is at stake. Were physical fitness works hand in hand with mental determination and analytical skills then I would say its a sport. If it is played to spend the wee hours of the day or to just enjoy it for friendships sake ...then its a game.lol