It sounds like their system may punish teams that are playing worse - you tend to get a lot of negative comments online if you're playing horribly (esp if nobody expected it). Also, they might be rewarding teams for having more positive comments (and obviously the Yankees have a huge fanbase).
This is a perfect example of how data can make a statistic... That's all it is. The Indians aren't the most hated team in baseball, unless you score the data a certain way and remove other data. The Yankees are easily the most hated, followed by the Red Sox... Everyone is "meh" except for your favorite team's rivals... That alone should've countered the red sox/yankees fans though, the loathing for the other from their fan bases... weird it didn't work out that way
I think this list is laughable, they have no real way to know which team are hates the most or liked the most. I hate it so much when people create stupid stuff like this list because it makes no sense.