Professional boxing, for example, has several world champions at different weights, but each one of them is decided by a "title match", not a tournament.
This is especially true of the "Big Four" major professional sports leagues in the United States and Canada; world cups and championships exist in all four of the major sports, but the domestic U.S. and Canadian leagues are generally known as the world professional championships (due to the best players worldwide being in the league itself) (as with the Stanley Cup, ostensibly an independent championship for ice hockey but under the de facto control of the National Hockey League through two trustees who since no later than 1947 have been NHL loyalists) or the equivalent of a world club championship.
In American football, although an IFAF World Championship exists, the United States is so far above and beyond the other nations it faces that the winner of the U.S.-based Super Bowl, a competition limited to the 32 teams in the National Football League, is commonly nicknamed as the world champion by the players, the press and fans alike; the NFL itself explicitly marketed the contest as a world championship in its first iterations.
[2] On the other hand, association football (soccer) has more parity between national leagues and even continental tournaments has seen the birth of one true "world championship".
[3] After that, there have been many tournaments between teams from around the world, but it wasn't until 1960 when the Intercontinental Cup was established, competed between the winners two greatest and most important continental championships: the UEFA Champions League from Europe and CONMEBOL Copa Libertadores from South America, the cup was endorsed by both UEFA and CONMEBOL but had no involvement from FIFA, the governing body for world football.