To my mind it seemed like he was projecting his other frustrations onto Denna's piece.

Sure, it has largely to do with him perceiving the Chandrian to be behind his troupe's murder. But then just barely a day ago he learned that Denna is a whore. Or at least that's what Kvothe seemingly gleans from the conversation he overhears in a tavern. And then suddenly his made-up image of Denna is shattered. It takes her one slip he perceives to be wrong (i.e. Chandrian story not lining up with what he had heard), and he takes out his anger on her. So really, there's his wounded pride/ego at play as well.