Pinning isn't magic; it's more like a "first strike" – a physical skill. It worked for me even without the Ring of Negation. Give it a try.

Yes, you're right. Sorry, I got fixated on the idea that nothing affects the Champions of the Deep, and everything is useless against them except brute force and numbers. Turns out that's not true! I just tested it myself and was pleased to see how a druid summoning mantises can tear these brutes apart.
So, it's mechanical damage. And it reduces the Champions of the Deep's movement speed. Plus, the shackles also reduce their damage output by half. But! Any action other than attacking will free the bound target. So, if you've pinned them, finish them off completely, as they say.