Why is a connection to Earth implied in this power supply
The reason the earth pin is at the input is because this particular power supply references its output voltages to it.  Note that the power supply itself runs from the L and N (line and neutral) inputs, and that it's output is isolated from them.  The outputs are then deliberately referenced back to the earth input line.

Some power supplies allow the output to float, others specifically reference it to something.  This is one of the latter.