You know if you change enough parameters in any definition you can get to the good ol' argument of what "is" is.
So now we are debatrng the definition of the word "game"? Your question was "is it a game?". The answer is yes. NASCAR is a game by the strictest definition of the word. There is a point system. There are mutiple oponents, there are definitely physical requirements including physical and mental agility. The fact that the vernacular doesn't include "the game" in reference to the event doesn't mean it isn't one.
Other things never individually refered to as a game by participants but are definitely sporting events:
Several dozen Track & Field events, Gymnastics, speed skating, Biking both cross country and velodrome events, Martial arts, boxing, wrestling, greko-roman, MOTORCROSS, and so on...
Really "the game" refers to football, baseball, Soccer (fútbol) and basketball. To some maybe hockey and lacrosse.
Now if you want to change your definition again. choose another word..
Any definition you can conjure up that removes motor sports as a sport removes other events that are considered sports by any thinking human.
BTW
I withdraw my statement about throwing the ball over the fences. I meant 390-435 feet (specifically I had 404' in my head) but I misstated it in my first post and everyone took it as the shortest possible babe ruth league 300 foot fence when I meant major leagues. And it really doesn't matter. The point was that there was use of a tool that allows for something that pure muscle, flesh and bone couldn't do for most but that point was lost.
Salsa's "muscle only" definition is as close as we get to excluding motorsports, but we have already established that one requires more muscle to wrestle a car around a track than one may think. It is NOT like driving on the freeway during rush hour.
See ya
Tony