Suppose a university has five departments (English, Math, History, Science, Engineering,). It has some rules that were applied to only English, Math, and History departments. But now, those rules are applied to Science, and Engineering departments too:
"The rules are now applied across the board, including Science and Engineering departments.
"The rules are now applied across the board, including to Science and Engineering departments.
Is the "to" necessary?
The "to" is wrong. You need a "the" before the names of the departments.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.