I don't feel like quoting Al's giant post, but its not the award for the best player in the league, its the one most valuable to their team.
If you took both Ortiz and A-Rod off of their respective teams and put in a random bottom of the rung player then you would clearly see that Ortiz did more for the Red Sox than A-Rod did for the Yankees.
A-Rod was the best player in the league this year, but the Yankees could have survived better without him than the Red Sox without Ortiz. The Yankees ship would have been sunk however without Mo Rivera.