Unfortunately, MLB is not making postseason.tv available on any devices other than mobile platforms (iPhone/iPad/iPod Touch) and PC browsers. MLB.TV subscribers using the Playstation 3 are in the same boat as our users. MLB support has explicitly stated that postseason.tv is not available on anything other than the above mentioned devices and they do not appear to have any intention of enabling it for PS3 or Roku users.
If you subscribe to MLB.TV, playoff games are viewable on the Roku player after the live games are over and go to archived status. Unfortunately, live games are blacked out due to MLB's blackout policy on nationally televised games.