Thanks for noticing that and bringing it to the attention of this forum. Unfortunately, where it says "Click here to watch games live", it takes you the MLB.com subscriptions page. There's no indication whatsoever that you can watch the game on iTunes. Also, the games won't be free: you have to subscribe.
Nonetheless, this is the direction that tv has to go to enable it to become mainstream. Live TV is not necessary most of the time; iTunes' à la carte model works brilliantly to replace the live broadcast + DVR model, but it misses out on what needs to be live: sports and news.
This could be easily solved by having streaming live video of sports, using MLB.com as a good example. Buy your game or a season and when the game is about to begin, tv could remind you. You can tune in immediately or watch it in deferred live (start when you want, even before the game ends).
It would be great to see SteveJobs announce this next step in the tv "hobby" at MacWorld in the next few weeks.