None of the other teams in the modern era that won 20 or more games won the World Series.
To expand on this a touch for the 19th-century teams:
1875 Boston Red Stockings (Braves) of the National Association. won 26 straight to kick off their season. They won the National Association at a resounding 71-8, 15 games over second place Philadelphia. No matchup with the American Association as it was formed seven years later.
1880 White Sox who went 21 straight undefeated with a tie at Providence 6/4/80, as game 2 of 21 of this stretch won the National League outright, at 67-17, also winning their pennant by 15 games, but in this case, the silver went to Providence. Like in 1875, there was naturally no with the American Association as it was formed two years later.
In 1884, there were actually two such streaks of 20 straight wins at 84-28, with the St. Louis Maroons of the one year Union Association (also had the first "MLB" 20 strikeout game by One Arm Hugh Daily) and the Providence Grays. The Maroons, led by Sure Shot Fred Dunlap, won the Association handily, finishing 94-19, 21 games above the second place Cincinnati Outlaw Reds. It was considered a lower quality of play below the AA and NL, although their strong play made them part of the National League from 1885-89. However, the Union Association also led to something interesting regarding the other team of note here, the Providence Grays, and an all-time MLB record. The Grays went on to win the National League by 10.5 games with a record of, with the Boston Beaneaters finishing second, eventually sweeping the American Association's New York Metropolitans 3-0.
As for the importance of the UA? Well, two SPs were the norm in those days. Providence had two: Old Hoss Radbourn and Charlie Sweeney. Lansche's
Glory Fades Away states that the latter got drunk, expelled from the team after lack of willing to be removed from the mound in the summer of 1884, and later signed with the Maroons. It left the Grays primarily only Radbourn to pitch the rest of the season, including all three games of the 1884 World Series. This allowed Radbourn to get the most all-time wins in a season, 59 or 60 (depending on your source and/or interpretation of July 28th), given how frequently he was used. As Radbourn claimed (and paid as much) he was doing the work of two individuals the rest of 1884, Radbourn was also given free release following the season, as per his request--almost a free agency style move, which piqued my fancy when researching this.
The 1916 Giants (26 straight wins)
Bit misleading, yeah? Sorry to be a bit nitpicky, but they were 26 games without a loss, Games 124-150 of the 1916 season, but not 26 wins straight. 9/7/16-9/18/16 Game 1 for 12 straight, then a 1-1 tie after 8 on 9/18 against Pittsburgh Game 2, then 13 more from 9/19/16 Game 1 to 9/30/16 Game 1.