What determines how faculty receive email for a given department?

The Classifications assigned to a person record determine which system group someone is added to, which — in turn — informs which departments the faculty member receives emails for.

The English department classification here includes this person in all emails sent to this department via the distribution list.  

If you remove the "Department: <DepartmentName>" classification from the record(s) who should not be included in the group and then run the Refresh Group Membership procedure from the System homepage action menu, they are removed from the group and will no longer receive emails via the group Distribution List.