Sounds to me like Jacob's game involves bringing people to the island and MIB's game involves convincing them to leave. Those who don't want to leave end up dead.
I don't think Widmore ever met Jacob. Just like Ben never met him. I think MIB, posing as Jacob, ordered Widmore to purge Dharma.
Side note: Did anyone else see last week's episode with the pop ups? I think there was a part that said Dogen has been on the island for almost 15yrs. That brings us back to 1992.