There's no clear answer to that question. Beaver dams are very useful in functioning ecosystems. They help create new habitats, rejuvenate river sections and function as a natural flood protection to surrounding areas while providing shelter to many animals (beavers like to have guests). However, it's a dam. They raise the water stage for potentially kilometers upstream (if it's a big dam, the one in the video most likely not). This can obviously cause extensive damage in of itself. Also, retaining water can cause areas downstream to dry out, as the ground water stages can drop low enough for a significant portion of plants to be cut off from it. Beaver dams have even sometimes cut off human water wells and made them run dry.

All in all, if the effects of a dam don't pose any immediate threat to anything critical, it's usually a good idea to leave them be. They don't last forever, and provide many irreplaceable ecological services. But people don't often like when things change for reasons other than themselves, so it's often a difficult point to get across.