Furthermore where does this information actually come from?
The information is downloaded from the Ubuntu servers provided that the developers set/uploaded it when they first added the application to the Software Center catalog.
Why don't the free applications get this feature?
As you can tell from Amnesia and other commercial apps, this "feature" lists primarily hardware requirements, not software. This is a separate Software Center catalog feature.
Software Center lists pretty much all the "free" applications via the standard repositories, and the standard "Debian" format they use does not have such a custom field (call it
Developers of free applications can certainly choose to provide this information if they separately upload the application to Software Center instead of relying on the standard repositories. If there is a specific free application you would like to see this for, please contact the developers.
Seeing software requirements (dependencies) for free apps
If you would like to see the software a free application depends on (and will install along with it), you can try using Synaptic - an alternative but slightly more complicated package manager.
I will use the free game ExtremeTuxRacer as an example - note the second screenshot in particular: