Thursday Nights they have an exclusive game with their crew. Saturday's they usually have a DH by using feeds from the RSN's. They have matinee games during the year and in September during the home stretch they had games of importance almost nightly. So its more than "1 game a week"
By 1 game a week I meant 1 exclusive game per week. The rest of the games can be viewed via the RSN feed provided you get that feed.
do people watch the NFL Network during the offseason? probably
MLB Net is the same way. They have lots of good programming during the offseason
DodgerKing listed some in this thread
I'm not sure if MLB Net can be compared to the NFL Network though. NFL season is almost year round due to the way the draft is run and the fanfare leading up to it. I can't even remember the last time an MLB draft even made my local news and aside from free agent signing or steroid aligations baseball doesn't even make the news at all.
And while I'm sure that this thread is catering to the die-hard baseball fans that would watch the channel in the offseason, the majority of people who would watch the network would be interested almost exclusively in that 1 game per week mentioned before, and even then it would be due to the it being the home team or gambling until September as I can't picture ever wanting to watch two teams I have no association with.