open-source developers are already writing code for free. ...On Linux, anyone can get the source and fix it, and someone will usually do so for free.
You're confusing open source developers with players of open source games / users of an open source platform.
At the moment open source is supported by developers for free largely because the
company fixing the bugs has some other way of making money from the open source platform.
For example an IT company deploys Ubuntu in its client companies; fixes bugs in Nautilus because they make money from a client that has a file browser that doesn't die. Everyone wins, and takes home a pay packet.
Sure there'll be the occasional hobbyists but they're not really what drives open source development. In my opinion.
So what's the model really?
Valve will take a cut of games they sell via SteamOS.
Paid developers will do a significant part of the work on SteamOS. They will be paid because they are games developers who sell games on SteamOS.
Game players will buy games on SteamOS.
A very small fraction of those game players will have the wit and know-how to make changes to source code. This is a volunteer coder.