It is insanely in depth. You have to know EVERY move the opponent can make at any time, know what would be best to counter, and since each opponent is different, you have only limited time to figure out how to best counter your opponent.
To compare time of chess, and time of ssb, you also have to take into consideration the game speed. Yes, chess may occasionally take longer, but it is also a slower pace. 15 minutes may not seem enough, but take into consideration the hardest AI the game has, I can be in under 2, and can occasionally beat 2 at the same time in under 2. Most of my friends I can beat in under three. I usually register over 80 button pushes a minutes (in a slower paced battle) not counting the analog stick.
The second of the series is more competitive so I going to talk about that one.
In the game you can dodge attacks, or shield them. If you shield you want to try to get a shine shield, which means you have to shield at just the right time, that way you can counterattack. You only have a fraction of a second after shielding to figure out if you shined or not. There is also airborne dodging. You can dodge in any direction in the air, sometimes to get up to a higher place, sometimes the opponent has a delay attack and dodging up will just barely allow you to escape the attack long enough. Then you have to fast fall and hope that you recover from the landing fast enough to counter.
I could make several pages just about dodging and shielding alone, all that have to be considered in an instant based on what you learned about your opponent, what you know about the opposing characters moves, what you know about strategies of that character, and what you know about your character and his physics with he game environment.
It is one of the simplest games as far as anyone being able to play it. 2 attack buttons, a shield button, and a throw button. Pushing a directional button changes that the attack and throw button does. But the depth required in just that is astounding. Even in a flat level, with no items on, all the possible things that need to be considered each and every second for competitive play, is exausting.
The last tournament I went to, I was exhausted when I finished. That was a local tournament as well. Not even a worldwide or nationwide one. I never went to one of those, never been one close enough.
Edit. Me and my friend stayed up 3 days straight playing spiderman 2 from beginning to end until we beat it 100%, When one of us wasnt playing he was eating and giving advice. I can play games for long periods of times no problem, but a tournament that lasted that long and that was all filled with high level players, that would be insane. It all depends on your competitiveness. I can play chess for hours and be fine, but Im nott doing it competitively. When I play games, I can do it for extended periods of times, but when I play competitively, its a whole new game.