The idea that a 10-person company of 20-somethings in Mesquite, Texas, could get its software on more computers than the largest software company in the world told him that something fundamental had changed about the nature of productivity. When he looked into the history of the organization, he found that hierarchical management had been invented for military purposes, where it was perfectly suited to getting 1,000 men to march over a hill to get shot at. When the Industrial Revolution came along, hierarchical management was again a good fit, since the objective was to treat each person as a component, doing exactly the same thing over and over.
The success of Doom made it obvious that this was no longer the case. There was now little value in doing the same thing even twice; almost all the value was in performing a valuable creative act for the first time. Once Doom had been released, any of thousands of programmers and artists could create something similar (and many did), but none of those had anywhere near the same impact. Similarly, if you're a programmer, you're probably perfectly capable of writing Facebook or the Google search engine or Twitter or a browser, and you certainly could churn out Tetris or Angry Birds or Words with Friends or Farmville or any of hundreds of enormously successful programs. There's little value in doing so, though, and that's the point - in the Internet age, software has close to zero cost of replication and massive network effects, so there's a positive feedback spiral that means that the first mover dominates.
If most of the value is now in the initial creative act, there's little benefit to traditional hierarchical organization that's designed to deliver the same thing over and over, making only incremental changes over time. What matters is being first and bootstrapping your product into a positive feedback spiral with a constant stream of creative innovation. Hierarchical management doesn't help with that, because it bottlenecks innovation through the people at the top of the hierarchy, and there's no reason to expect that those people would be particularly creative about coming up with new products that are dramatically different from existing ones - quite the opposite, in fact. So Valve was designed as a company that would attract the sort of people capable of taking the initial creative step, leave them free to do creative work, and make them want to stay. Consequently, Valve has no formal management or hierarchy at all.
I wonder if Tim Cook's recent visit to Valve is less about collaboration on specific products and more about Apple's curiosity about their process. (Probably not, but fun to think about.)