Win is 1 point, draw is 1/2, loss is 0.
The only elimination tournament I know is the 128 player world cup. Very tough to win because one loss and you're out!
For us amateurs, we're usually playing a swiss system. Players are seeded according to rating, and then the list is cut in half. The top of the bottom half plays the top of the top half and so on down the list. For the subsequent rounds players are paired with opponents who have the same score (1.5s are paired with other 1.5s, 3s are paired with 3s, etc). Yes, many times there are large ties for 1st, 2nd, and or 3rd place. But everyone gets to play every round.
Top pros usually play a round robin (everyone plays every other player once) or a double round robin (everyone plays every other player twice, once as white and once as black).
The most similar to tennis would probably be match play where the players play a series of games alternating black and white. This is how the world champion is crowned. Minor matches may only be 2 games long. World championship matches have varied over the years. Not so very long ago they were 24 games. Present day uses half that, 12 games. One game is played a day, with a few rest days here and there.
In tennis you need to win either three set (or two if it is best of three match). How it is in chess? Who wins the whole battle? Is it so that from draw you get one point and from winning two? How many is needed to win the whole battle?
In tournaments I guess there is different systems: every player play against each other once? And then there could be cup tournaments? Winner survived to next round.
Of course always can be played only one game, but I guess it is so only among hobbyist.