I asked what he thinks other economists think the market is if not a process, and I'm still not quite sure what his answer to that is. I certainly view it as a process. I'm not even sure what a theoretically viable alternative answer would be!
The discussion takes two diversions that I think are unhelpful, but I suppose might shed light on what he means:
1. They discuss the sorts of issues economists look into
I would agree that Austrians talk about the market process itself a lot more than most mainstream economists. This is true. But I don't think you can draw the same conclusions from that many of the commenters try to draw. At work we evaluate a lot of federal programs. There are two major components to an evaluation: an impact analysis, and a process analysis. I mostly do the statistical work on the impact analysis. What actually happens at these federal programs is usually a black box to me (sometimes we empirically model the process itself, but usually not - we just get at it through interviews and focus groups). My job is just to use econometrics to produce a defensible estimate of the impact a program had. Now, the fact that this is what I spend a lot of my time working on that doesn't mean I don't understand there is a very complex process that is going on in these programs. It's just a scientific division of labor. I'm better at running the numbers. I've interviewed for the process studies on a couple of occasions and it was a good experience, but it wasn't really my strong suit. I'm the only junior staff in my center right now that knows how to implement a regression discontinuity design or do propensity score matching. It figures they assign me to do that stuff.
Evolution is fundamentally a genetic process. There are lots of biologists that aren't geneticists. It doesn't mean they don't accept or understand that evolution is a genetic process. Weather is fundamentally just classical mechanics - it's physics. Meteorologists aren't primarily Newtonian physicists, but this doesn't mean they don't understand the nature of that underlying process.
Where does this market process focus get you, though? Not very far in my opinion. If that's an interesting question to them, that's great. I think there are other more fruitful things to look into, and you can get a lot of mileage answering the really interesting questions out of the parsimony of neoclassical models than you can out of the richness of a poetic prose treatment of discovery, surprise, etc. I have a lot of questions I find interesting and want to answer in my career (1.) why is there excess worker reallocation, and how does it vary over the business cycle? (2.) what role do worker flows play in price level adjustment?, (3.) what is the impact of the job creation tax credits that have been implemented?, (4.) how do scientists and engineers select into technical and managerial occupations?, (5.) why are African Americans so much worse of economically in the United States? (6.) what happened to the American economy between 1919 and 1922?, etc. etc. I don't see how process theorists like Mises or Kirzner can really help me with most of these problems. There could be some applications, but it doesn't seem like the best way to answer the questions that I find truly interesting. Not to mention the fact that market process theory doesn't have any insights into the intellectual history that interest me - the intellectual history of Keynesianism.
What I find scientifically interesting seems like an odd metric for whether I think the market is a process or not.
2. They discuss modeling
The other thing that came up in the comment thread was modeling. Akerlof completely oversimplifies things and never talks about alternatives therefore he doesn't see how complex the market is and that the market is actually a process, etc. etc.. You all have heard the claim before. I don't know why this is such a stumbling block for people. Human society is incredible complex and if we want to understand it scientifically we have to explore questions parsimoniously. Parsimony in exposition is not the same thing as an oversimplified understanding. Yes, models simplify things to highlight specific mechanisms operating in the economy. This is a feature, not a bug. People need to deal with it. We've known about government failure and market efficiency for centuries. This is the foundation of the discipline. Everyone knows this stuff. When Akerlof and Stiglitz were starting to write about information asymmetries that was a genuinely new insight and mechanism they were exploring. Constructing simple models to illustrate the process and understanding the role it plays was excellent science on their parts. It certainly had a higher marginal benefit than someone who spent their time telling us more about what we already know about government failure or market efficiency.
I called this post "the market process and blue skies" because this post from Boettke reminded me of the debate that he had with Bryan Caplan a while back (part 1 is here). I don't always agree with Caplan, but I thought he did incredibly well in this debate - particularly in the debate portion (I was less impressed with the performance during the Q&A, but I imagine that's a lot harder to do). Anyway, one of the things Caplan says is that a lot of Austrian claims are of the "Hayek said the sky is blue" variety. There are lots of claims that Austrians make that basically everyone agrees with and has agreed with even before there was an Austrian school. But if Hayek said it at some point it somehow becomes owned by the Austrians. The market is a process, values are subjective, socialism doesn't work, etc. etc. Anway, it's good stuff.