I think the argument is that there are objectively measured sports and subjectively measured sports. If you and I are competing in the javelin, there is no "judging", except to determine faults. If I throw farther, I win. So track sports, swimming and so forth are objectively judged. The same goes for volleyball, baseball, soccer, etc: the points determine the winner.
Sports like diving and gymnastics are heavilly based on style and a point system that is largely subjective. A triple whatnot is given a "DD" rating or something by a judging committe because it's harder than a double whatnot with a twist. Then points are added and dropped based on how /well/ you do a triple whatnot.
Wheter or not subjectively scored sports are really "sports" or not brings up the old argument as to what a "sport" consists of. Is curling a sport? Is paintball? Tag? Golf? Auto-racing? Chess? If I invent "full contact chess" does it elevate chess from game to sport? Your answer depends on how much of a fan you are and how much you understand the sport. NASCAR would seem to me to be an exhibition, its not a measurement of physical skill, it seems to be more about strategy and control. But I'm neither a fan nor an expert.