We believe (a) that there is no separable essence of goodness, but also (b) that there are moral facts that people can be wrong about. I think the general public understands "moral relativism" to exclude (b)

I think that's uncharitable to the public: surely everyone should admit that people can be mistaken, on occasion, about what they themselves think. A view that holds that nothing that comes out of a person's mouth can ever be wrong is scarcely worth discussing.

Eliezer doesn't define morality in terms of humans; he defines it (as I understand) in terms of an objective computation that happens to be instantiated by humans.

The fact that this computation just so happens to be instantiated by humans and nothing else in the known universe cannot be a coincidence; surely there's a causal relation between humans' instantiating the computation and Eliezer's referring to it.