This is similar to "classical music". For those farther removed from this discussion, "classics" would include Shakespeare just as much as classical music would include Bach. No point in arguing "well, he's really Baroque".

You're conflating two things here re: classical music. There's classical music, the genre, which includes the Classical Period as well as The Baroque, Romantic, and Modern periods.

Admittedly, this is really confusing, and it'd make a lot more sense to call one of those "classical" things something else, but I'm not in charge of naming things (any more).

> For those farther removed from this discussion, "classics" would include Shakespeare

I think for a academic department, Classics would be Ancient Greece and Rome, not Shakespeare (which would be in the English department).

Sure but if the article is about a “baroque department” being eliminated it becomes a distinction with a difference.

I edited my post a little though to address that West is talking about both, but only one is actually in danger.

Not so. A "classics" department in a university is focused on greek and roman language and literature. Shakespeare is a thousand years too late.