I haven't read every post in this thread, so apologies if this has already been said. I think "sport" is too broad a category. When automobiles are compared, a Yugo is not compared to a Ferrari. They are compared to others in their class. I would break classes down into something like this:
Sports: baseball, football, basketball, hockey, tennis, swimming, skiing, track and field, and so on with physically demanding competition,
Games of skill: golf (arguably a sport), billiards, darts, bowling, curling, shooting, shuffleboard, others that require a measure of fitness and coordination,
"Board" games: chess, checkers, backgammon, casino games, crossword puzzles, sudoku, others that require no physical skill other than some stamina in a long tournament.
IMO, golf is the most difficult of the games of skill, followed by billiards.