The third wire in the psu cord is ground, and is directly connected to the psu case and all of the black wires coming from the psu. This can be easily verified with a $20 multimeter.
When the components for a computer are wired together, they have all the ground needed to function properly, even if they are just laying on a wood table, for example.
When the components are mounted together in a metal case, a redundant ground situation is created, and the case is grounded as well to prevent EMI radiation and reduce shock hazard.
To duplicate the redundant ground scenario using a wood case you can install wires from the psu case to the mount screws on each component using serial and/or parallel paths. This is not necessary from a shock hazard point of view, and does virtually nothing to reduce EMI. It might help reduce equipment risk to static electricity.
Hope this helps.