To me, a sport is an organized activity in which two or more people compete against each other in achieving a common goal using personally developed physical and mental skills to gain an advantage over their opponent, and the end goal does not involve the death of any player. This excludes, however, anything that simulates a physical scenario by electronic means (like a video game). That's a simulation of a sport. Airsoft, I would say, is definitely a sport.
People play "sports" all over the world on a day to day basis without "set" rules, and that doesn't make them cease to be a sport. For example: how many variations are there of football with different set rules? NFL, CFL, Arena, College, High School, Flag, etc. If I decide to play 2 hand touch football, is it not considered a sport anymore? Even professional sports sometimes have variations in their rules from location to location. Pool is governed by "house rules" depending upon where the tournament is, baseball's home run line varies according to the ballpark; sports like hockey and soccer have completely different rules in the Olympics than normal. Also, a sport doesn't have to be a spectator activity.
Another thing: it drives me crazy when people try to argue airsoft as a "sport vs. hobby," as though it can only be one or the other. Goodness, a sport IS a hobby!! Some people are fortunate enough to also make a sport their career, but for the rest of us, it's a hobby. Airsoft by itself (collecting, upgrading, accessorizing) is just a hobby, not a sport. When you involve other people and use it competitively, it becomes a sport.
-BATMAN