The Cubs' win was announced in the INSIDE SPORTS box-out in the top left-hand corner of the front page of the October 22, 2015 issue of USA Today.
The Chicago Cubs last won the World Series in 1908. On October 13, 2015, the Cubs defeated the St. Louis Cardinals in Division Series play after winning their Wild Card. They moved on to the National League Championship Series in late October. On October 21 itself, the Cubs were playing the New York Mets at game of the NLCS, having lost the previous 3 games. The Cubs lost in Game 4.
The Cardinals are the team supported by Back to the Future writer Bob Gale. (in a bit of irony, director Robert Zemeckis is a Chicago native but favors the cross-town rivals White Sox) Gale explained that since the movie was set in October, it had to feature a World Series joke, and the Cubs were the winners because "what could be more insane than that?"
Though the film correctly predicted that an MLB team would exist in Miami by 2015, it would not be possible for the Miami Marlins to play the Cubs in the World Series, as both teams play in the National League. In the 2015 season, Miami failed to make the playoffs, but did a season-long "Rewrite the Future" promotion, and hosted a Back to the Future night featuring appearances by Bob Gale and Claudia Wells, in the hopes of "changing the future".
The 2015 World Series began on October 27, and concluded on November 2, two weeks later than predicted in the film. This is because the Division Series did not exist until 1994, nor the Wild Card Game until 2012. The placement of the World Series would have been correct otherwise.