Maybe Eliezer would say that he is a "subjective realist" or something like that. This is strictly different from moral relativism, where choice of morality is more or less arbitrary. As a subjective realist your morality is different than your pebblesorter friend, but it's not arbitrary.

Philosophers just call this position "moral subjectivism". Moral realism is usually defined to exclude it. "Relativism" at this point should be tabooed since no one uses it in the technical sense and the popular sense includes a half dozen variations which are very different from one another to the extent they have been defined at all.