I was curious about it too and there was a paper about it with the following summary:

Valve is a “flat” company without a management hierarchy or traditional boss roles: instead of top-down organization and management, Valve employees are free to work on whatever projects they choose and to convince other employees to join collaborative groups. Decision-making is thus “democratized” rather than centralized in key management positions. This peculiar structure, or lack thereof, seems to challenge conventional ideas about organization not only in the video game business but also business in general.

The code is so old that their developers are already dead.