The published version can be found here. Link rot protection: the link is to the Journal of Cognitive Science, vol.12, issue 4, 2011. That issue and some subsequent ones contain responses to Chalmers and Chalmers' response to the responses.
I'm having difficulty in seeing how the paper says more than simply that the mind is a physical process. According to his definitions, all physical processes implement computations, and it is not clear that the mind specifically should be described in those terms, any more than the rest of the world. But perhaps mental physicalism still needs to be expounded, perhaps even more so in 1993 when the paper was written. The last 20 years of neuropsychology, though, takes that as a given, just as molecular biology takes for granted that living things can be explained in terms of being built from atoms.
I'm looking forward to checking out the responses you linked to.
One implication of the paper that I found interesting is that not every physical process implements every computation or even every computation of a comparable finite size. Thus, I find Chalmers' paper to be the most satisfactory response I've come across to Greg Egan's Dust Theory, previously discussed on lw here. (As others have anticipated though, you do need to grant a coherent and not-too-liberal notion of reliable causation, but we seem to have ample evidence for that.)
For many scientific interests, I agree that it may not be necessary to describe or conceive of the mind in these computational terms. But if one is engaged in a grand reductionist project comparable to reducing neuropsychology to molecular biology to atomic theory, then, well, it helps to have the equivalent of a precise atomic theory to reduce to. For the purposes of my philosophical research, I'm reducing metaethics to facts about the cognitive architecture of our decision algorithms, which in turn are reduced to certain kinds of instantiated computations, which are reduced a la Chalmers to physical processes, which I take to be modelled by Pearl style causal models allowing us to be otherwise agnostic about the level of explanation.
A Computational Foundation for the Study of Cognition by David Chalmers
Abstract from the paper:
Computation is central to the foundations of modern cognitive science, but its role is controversial. Questions about computation abound: What is it for a physical system to implement a computation? Is computation sufficient for thought? What is the role of computation in a theory of cognition? What is the relation between different sorts of computational theory, such as connectionism and symbolic computation? In this paper I develop a systematic framework that addresses all of these questions.
Justifying the role of computation requires analysis of implementation, the nexus between abstract computations and concrete physical systems. I give such an analysis, based on the idea that a system implements a computation if the causal structure of the system mirrors the formal structure of the computation. This account can be used to justify the central commitments of artificial intelligence and computational cognitive science: the thesis of computational sufficiency, which holds that the right kind of computational structure suffices for the possession of a mind, and the thesis of computational explanation, which holds that computation provides a general framework for the explanation of cognitive processes. The theses are consequences of the facts that (a) computation can specify general patterns of causal organization, and (b) mentality is an organizational invariant, rooted in such patterns. Along the way I answer various challenges to the computationalist position, such as those put forward by Searle. I close by advocating a kind of minimal computationalism, compatible with a very wide variety of empirical approaches to the mind. This allows computation to serve as a true foundation for cognitive science.
See my welcome thread submission for a brief description of how I conceive of this as the first step towards formalizing friendliness.