Whether something is a sport or not depends entirely on the participating individuals’ approach towards it. If you train for it, practice it, and compete in it, then it (the game/sport in question) is a sport. If you do it recreationally because it’s Saturday and it’s nice outside, then it’s a game.
(EDIT: Upon rereading, this first paragraph doesn’t make a whole lot of sense. I should have said that whether or not someone is an athlete in a given sport depends on their approach to the sport.)
Also the game/sport has to require some level of athletic skill in its performance.
Athletic skills: endurance, strength, power, speed, agility, coordination, balance, and accuracy
Tiger Woods is an incredible athlete at the sport of golf. Tiger Woods is as good of an athlete at golf as Michael Jordan was in basketball. Hence the fascination with him. He is a once in a generation talent at his chosen sport (golf requires balance, coordination, and accuracy, hence it is a sport).
I read something a while back on the different levels of competition and how far removed they are from the most basic level of competition. They went something like this (to the best of my memory):
Level 0: Hand to hand combat, no rules (not a sport; this is combat)
Level I: Hand to hand combat, only cheap modes of attack made illegal (MMA)
Level II: Hand to hand combat, one specific discipline (boxing, wrestling, BJJ, muay thai)
Level III: Direct competition using physical contact as a primary means (football, rugby, hockey)
Level IV: Dircet competition with most physical contact outlawed (basketball, soccer)
Level V: Indirect modes of competition with objective scoring (golf, weightlifting, track and field, etc)
Level VI: Indirect modes of competition with subjective scoring (gymnastics, figure skating)
The only time the issue of whether something is a sport or not comes with levels 5 and 6.
