I think the general use of the word means 'an active contributor to the competitive scene'.
If you don't like that, here's how I think of it. I'll redeem Wintermelon43's comment as an example.
You're breathing. Why?
If you answer "because I want to beat death" then you are the low form of competitive. These players enjoy winning. They will stop playing if they consistently lose. While this is assuredly not always true, they are often lackluster fighters and lackluster people.
If you answer "because there is so much that I must do" then you are the high form of competitive. These players enjoy finding and pushing their limits, and tournaments and the like give them a chance to showcase their skills. They will stop playing if they themselves aren't doing well or the opponent is playing in such a way that they cannot well perform. I think most top players are in this category.
If you answer "because the air smells nice this time of year" then you are a casual. These players enjoy Smash's combat, and they don't care whether they win or lose so long as the fighting is good and exciting, with lots of hard reads and falcon punches. They will stop playing if the opponent is camping or spamming projectiles or rolls because then there's no proper fighting.
So it depends on where your priorities lie. Of course, merely because you're high competitive doesn't mean you can't enjoy Smash for Smash's sake, nor does being casual mean you place no value on your performance, nor does preferring winning over losing mean that that's all you care for.
