Voltage Converter's GND Problem
The voltage converter circuit shown, like most (safe) DC adapters in domestic or retail use, is an isolated power supply - in other words, the voltages are isolated from any reference to the power supply lines, including the building earth line.

From the circuit's point of view, the only reference voltage is the 0 Volt on the output side. Voltages are measured from a convenient reference, and electronic devices (usually) only care about this reference level. This does not need to be referenced to building earth, and should not be. 

The isolation protects the users of the electronic device, since touching any exposed metallic part of the device will not cause a shock: The voltage will not find a path back to the mains supply through the body.

Yes, you will find some transformers, especially high power ones, to have a high resistance connection from the secondary side to the supply earth, so as to allow a leakage path for the secondary side voltages to reference themselves loosely to building earth. 

This kind of high resistance path, or a similar mechanism, could be used to reference your "isolated" output side of the power supply, or the circuitry connected to it, to building earth. However, this is of limited merit and very occasionally done, other than for relatively high power equipment such as a drill. Note that this won't leave the output circuit properly isolated any more.