King Runeard's dam was in some way a serious constraint on their way of life if not an outright existential threat. They were aware it had been intended to be such, and they were essentially at war with Arendelle.
Whether or not they were aware that there were populated areas downstream (perhaps the lost Arendelle soldiers told them), they had ample justification to destroy it. In fact given that the stakes could not be higher for them (they had killed the king after all) they could reasonably believe that their only chance of survival was to destroy Arendelle.
As animists with an intimate and direct relationship with the forces of nature, they might have been able to get the rock giants to destroy it for them simply by asking. If not, someone could have done what Anna did: stand near the dam and provoke them into throwing rocks.
Out of universe, the dam had to be there because the plot hinges on a bold, sacrificial, not-counting-the-cost (if not somewhat reckless) action by one of Runeard's descendants, righting a past wrong by destroying the dam. But in universe it seems the Northuldrans were easily capable of doing so themselves. It seems odd that they didn't. Is there a known reason for that?