Having thought about it some more... Eliezer (and Scott Aaronson in The Ghost in the Quantum Turing Machine) agrees that free will is independent of determinism (since being forced to act randomly does not mean that you choose freely), so that's reasonably compatibilist. Here is a quote from the above paper:

Like many scientifically-minded people, I’m a compatibilist : someone who believes free will can exist even in a mechanistic universe. For me, “free will is as real as baseball,” as the physicist Sean Carroll memorably put it. That is, the human capacity to weigh options and make a decision “exists” in the same sense as Sweden, caramel corn, anger, or other complicated notions that might interest us, but that no one expects to play a role in the fundamental laws of the universe.

The introduction to the paper is also quite illuminating on the subject:

In this essay, I’ll sharply distinguish between “free will” and another concept that I’ll call “freedom,” and will mostly concentrate on the latter. By “free will,” I’ll mean a metaphysical attribute that I hold to be largely outside the scope of science—and which I can’t even define clearly, except to say that, if there’s an otherwise-undefinable thing that people have tried to get at for centuries with the phrase “free will,” then free will is that thing! More seriously, as many philosophers have pointed out, “free will” seems to combine two distinct ideas: first, that your choices are “free” from any kind of external constraint; and second, that your choices are not arbitrary or capricious, but are “willed by you.” The second idea—that of being “willed by you”—is the one I consider outside the scope of science, for the simple reason that no matter what the empirical facts were, a skeptic could always deny that a given decision was “really” yours, and hold the true decider to have been God, the universe, an impersonating demon, etc. I see no way to formulate, in terms of observable concepts, what it would even mean for such a skeptic to be right or wrong. But crucially, the situation seems different if we set aside the “will” part of free will, and consider only the “free” part. Throughout, I’ll use the term freedom, or Knightian freedom, to mean a certain strong kind of physical unpredictability: a lack of determination, even probabilistic determination, by knowable external factors. That is, a physical system will be “free” if and only if it’s unpredictable in a sufficiently strong sense, and “freedom” will simply be that property possessed by free systems. A system that’s not “free” will be called “mechanistic.”