Is the verb resumes in "College resumes Monday" transitive?

You are correct. "Resumes" is intransitive in this case, and "College resumes on Monday" is the full form of this sentence. However, when referring to days of the week, it is pretty common practice to drop the "on".

As you can see, dropping the "on" is a bit less common (at least in the case of resuming [on] Monday), but it is still a well-understood way to say the same thing.

The correct form would indeed be

College resumes on Monday.

However, the preposition can sometimes be omitted, especially in news headlines. But that doesn't make Monday the direct object of resume.

The verb resume can be a transitive verb, too. For example:

The program resumed its work.