Although by all terms this is simply a discussion about semantics, the fact that it can be applied to basically any activity is quite interesting. johann's post could (not saying he is) suggest a sort of spectrum from physical to mental exertion.
By this logic, one could say if an activity is a sport based on whether physical and mental exertion is more required in relation to the other, and we could define sport this way:
Most physical < - - - - - - - - - - - - - - - - - - - - > Most mental
I'd like to shift the topic to a slightly more focused question: On the 20-point bar above, where would chess be placed? Where would football, baseball, etc. be placed? What about Elements?
I would have to disagree with your straightforward approach. An example is cross country and distance track, Anyone who has done any sort of distance race knows there is a huge mentality aspect to the sport. Without a mind that can endure the physical pain, or the mentality to not give up when you know you have gone into oxygen debt. I would argue that it is more mental than physical.
A famous runner although not really a favorite of mine is a great example, Dean Karnazes and ultra marathoner.
"Karnazes was not compatible with his high school track coach and stopped running for fifteen years.[2] He resumed running on his 30th birthday with an impromptu all-night, 30-mile trek in his underwear and old lawn-mowing shoes."
This guy hadn't run in 15 years, and yet goes out and runs 30 miles in shitty shoes. He was not in extremely great athletic shape, he just had extremely strong willpower. The point of this is you dont become a good runner for being in great shape, it takes a mind that is focused and trained to perform such actions.