Sometimes it shines through, I agree. But I see it more in stuff like the flood of skulls in Return of the King. Or the bug pit scene in King Kong. He likes over the top gruesome stuff.
But action and conflict, that's not really a specific slasher director trademark, in my opinion.
I was actually surprised that The Fellowship of the Ring, one of the best films ever made IMHO, came from the director of Braindead and Frighteners. It's just so far away from and so high above the stuff he did before.