My personal definition of competitive consists of a few points.
1. High skill ceiling. If a game is built around the highest levels of play, you give depth to your hardcore audience that will be playing for years (see Starcraft, Halo 1+2).
2. Balance. If characters aren't properly balanced, you'd have a game that only supports a very limited variety of playstyles which leads to two related problems: a stale metagame and a small skill gap. If there's a small skill gap, good players aren't rewarded for learning and playing the game, and aren't encouraged to continue playing competitively. Stale metagame results in a loss of longevity, and this loss of longevity means that no one wants to play your game long enough to be competitive (see Halo 4's competitive scene dropoff for an example of a lack of longevity due to poor balance).
3. Approachability. If no one wants to play your game in the first place, no one is going to like it enough to be competitive in it. This is where casual players are very important, because when they pick up the game, play it, and want to play it more, which leads to them turning into competitive players. If they don't want to be competitive, they still have a blast. This is where Smash games have an advantage over some traditional 2D fighters like Street Fighter (which generally have a pretty steep learning curve) because it's incredibly easy to pick up and play. This larger playerbase can lead to a larger competitive scene, thanks to its accessibility.
To sum it up:
Casual players get "let's all play as Pichu in Lightning Mode with only bunny ears for items!" and have a fantastic time.
Competitive players get a deep, thought-provoking metagame that they can sink their teeth into and evolve for years after the casuals have moved on and have a fantastic time.
Again, this is my personal feelings on the matter, so take it with a grain of salt, but think this is what people are talking about when they say they want a "competitive" Smash title. Hope it didn't ramble too much.