Home-field advantage can be downplayed at times in baseball, but you would still rather have it than not. Aside from the obvious impact that fans can have, the home team bats last, so in an extra inning game it is an advantage to be the home club. If you score, the game immediately ends.
The Los Angeles Dodgers entered play with a one game lead over the Indians for home field advantage throughout the playoffs, they also hold the tie breaker.
Even if the Tribe cannot catch the Dodgers, they would have home field advantage in the World Series over any National League opponent other than the Dodgers.