When it comes to defining the name of a sport, the sky is ultimately the limit.
A physical element is always an obvious component. How else could a person use the word "athlete?" Using physical activity allows for a wide spectrum of events that can be defined as a sport: golf, hockey, baseball, football, soccer, tennis, curling, bowling, basketball, etc.
Risk should also be a factor when deciding if it is a sport. It should be something that leaves you at risk of injury during the event. A broken bone, a concussion, death—anything that could alter your life.
A sport needs to be real. That is why I feel it's wrong to call wrestling one. I'm not talking about the sumo or the kind that you take lessons for. I mean the stuff you see on TV, such as the WWE.
If a sport is real, the events and consequences are random and unplanned. Nobody knows what the outcome of any single move will be.
Mental strength at all times is another definition. Even if a "sport" has some physical need, you have to have a strong mind. You have to be prepared and keep your cool. You can't ever become bored with a moment.
A sport should be life-long. You have to work your way up, and practice for it harder than anything else. It is not something you could just start overnight.
It also has to be something you could make a living out of. Even if the money aspect isn't millions per year, it's your only job. It's a job you have as your occupation longer than anything else in your life.
It should always fill you with happiness. Feel proud of doing what you do. Play to win, but do not be too upset and quit if you don't. And of course, make the goal to become the ultimate champion.
I think if it fits the majority of the definition it should be considered a "sport." Poker is, video games are not. Bowling is, bar games are not. You get the point.