The first rule of sport is that it be a game. This could also include fighting, which would be sport at its most extreme.
Sport should be won by the participant that has displayed the most skill and physical ability, and this is ultimately true with fighting were you would expect the person with the most skill and physical ability to win the fight.
Sport should also be entertaining to spectators, and from the school playground to Roman amphitheatres nothing has thrilled crowds more than the spectacle of sport at its most ultimate. The most ultimate being a good old fashioned fight.
Sport can be participated in at an individual level, or as part of a team. Team sport at its most ultimate would be mob fighting, which if legal would draw in far bigger crowds than two individuals fighting. Possibly the closest thing we currently have to mob fighting might be tag team wrestling.
Sport usually has more than one participant and is usually part of a tournament set up such as a league or knock out competition. The objective is to win the tournament and be announced champion in that field. Taken to the ultimate, the objective would be to be named hardest person in the world.
In order to excel at sport you usually require key attributes such as athleticism and dexterity, and also intelligence. It is inconclusive which attributes outweigh the other. Sometimes a person with lots of experience and intelligence may defeat a person with lots of physical ability and athleticism. on other occasions a person with lots of physical ability and athleticism may be too much for a person with lots of experience and intelligence to handle. Taken to the ultimate there is only one way to resolve this dispute and that is to get in the ring.
However, usually what seperates sports from illegal fighting is the adherence to rules and customs. Real fighting has no rules and no customs and the winner can only be decided when one surrenders, is incapable of continuing or people from the crowd have intervened.
The downside of rules and customs is that we are not always getting a true reflection of what would actually happen without the intervention of a referee.
Sport should also usually come with a reward for the winner. With rules and customs that reward is usually a trophy for the winner and medals for the runners up. Taken to the most ultimate sport would be a gamble between two participants betting on themselves with the winner taking everything and loser losing his/her money. Though under current rules and regulations this would be considered illegal unless the bet is placed in a licensed premises. Two individuals putting money in to a pot with a winner takes all agreement is the equivalent of pool sharking. Something which goes on regularly in most pubs with a pool table.
Football has likely became the most popular sport as it contains elements of every single attribute you could think of which are required to participate in sport.