Do Dunwich monsters get removed from gate closings?
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 &quot;in Arkham&quot;, and would be removed.