In super smash bros tournaments, do they have a ranking system (for example, Elo)? what is it?
Elo is used for multiplayer(online) to find similar opponents.
What I think you are trying to ask is how are players put into the initial fights in tournaments, if that is your question then the answer is "seeding"
Basically on pools each pool will have at least one or 2 (sometimes 3) top players from previous tournaments. This will ensure that all new players(assuming bad players) to tournaments get weed out quickly and after pools brackets will most likely have all top players from each pool.
What "seed" avoids is having top players in the same pool, and having a pool with all new players, in such scenario new players will get very far without any struggle, and top players would lose very quickly, and the brackets will have new(bad) players vs top players... which would be very boring to watch.
Locally scenes rank the top players using Power Rankings (PR). Usually this consists of the top 10 players, but sometimes extends as far as top 16 or top 20 with the possibility of honourable mentions. This is used to seed the top players at local tournaments, as well as to give Tournament Organizers (TOs) outside the region an idea of who is good in a given area. Outside of PR, there are other rankings that are used namely the Melee it on Me rankings for Melee, and the Panda Global Rankings for Smash 4 which outline the top 100 players in each game.
Local PRs and the lists above can be voted upon by top players taking into account tournament placements, wins, losses, and perception of skill, but there are also some that only take into account tournament placements using an algorithm. The method used to decide the PR is generally at the discretion of the TO.