When a gate is closed, do matching monsters in Dunwich get removed? I'm aware the monsters in Dunwich do not count toward the monster limit as the vortices handle that dynamic. I would think the gate closing does affect all monsters across both boards.
Yes, monsters on the Dunwich board would also be removed.
From the Arkham Horror Rules (page 18):
Monsters and Closing Gates
When a gate is closed, all monsters in Arkham, the Sky, and the Outskirts that have the same dimension symbol (see “Monster Movement,” page 10) as the closed or sealed gate are removed from the board and returned to the cup.
and from the Dunwich Horror Rules (page 5):
The Phrase “in Arkham” on Cards
Cards that refer to “Arkham” also apply to locations and areas in Dunwich.
Thus all monsters on the Dunwich board are also considered to be "in Arkham", and would be removed.