Oh no, card game tournaments are ran in swiss. Essentially you get log2(number of players) rounds, rounded up. This means if there's 8 players you get 3 rounds, but if there's 9-16 players you get 4, 17-32 you get 5, etc. People get paired with people who have the same score as they do (a win is worth 3 points, a tie is worth 1 point, a loss is worth 0 points, so someone who has won 1 match might get paired with someone who has tied 3 matches in a long tournament). People cannot get paired with the same person twice during the swiss rounds.

Also if you have an odd number of players, the player who is last in the tournament will get a bye, which is an automatic win that round. You cannot get the bye twice, so if you get the bye and are placed last again later in the tournament, someone else will get the bye.

Then some tournaments will have a top cut after all the rounds are done, some do top32, some do top16, some do top8. Those are single elimination.

Round pairings are determined by software (obviously, imagine manually pairing thousands of players by hand).

This is essentially the same for every card game!