How does earth ground complete the circuit?
Where is that quote from? It is self-contradictory, and pretty much just plain wrong.

Current will flow if a load is connected between a generic power supply positive and negative, no ground connection is needed, unless you have some special purpose power supply.

A ground connection is often used for safety, especially in line non-isolated supplies, or as a means to reduce noise.  Even so, not all supplies pass the ground on to the output terminals or even make it available (for common examples, think wall-warts and such with just a two pole output).  Many supplies don't even have an incoming ground terminal from the mains (small switchers, and again, wall-warts).

I was going to post this as a comment, but it seemed to cover the question.

Edit as per comment below and corrected text.

Well, that does change things.  Generally, a DC power supply has no output tied to ground, or connected to the supply electrically at all, so connecting a load between an output and earth ground would result in no current flow.  Supplies that have an output set of terminals and a separate ground can often be configured (by jumping ground to one of the output terminals) as positive ground or negative ground if desired.