"Published scholarly research" — does "published" mean peer reviewed?

Not necessarily.

There are different kinds of academic publications.

• Peer-reviewed journal articles — yes, they normally undergo anonymous expert review before publication.
• University press books — usually are not "peer reviewed" in exactly the journal sense, but they are evaluated by expert reviewers before publication.
• Scholarly monographs — normally receive expert review through the publisher.
• Edited book chapters — usually reviewed by editors and sometimes external reviewers.
• Documentary editions — edited collections of original documents prepared according to scholarly standards.

So "published scholarly research" means research accepted by the academic community through recognized scholarly publication, not simply appearing on a website.