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Is that why a quick google search of "Poynting energy" or "Poynting vector" turns up the usual host of "over unity" websites?

This isn't the same thing at all.

Imagine, all your life that all you have seen was the interplay of light and shadow on a wall. You can theorize a light source. Then, along comes a theory that states that there is an entire room beyond that wall that you have never seen, can never see, and nothing you have currently done in the realm of experimentation can show you anything in that room. However, if you put your hand on the wall, you can feel heat and predict how it interacts with the wall.

Gravity would be the heat. The wall would be space/time. The "source" of gravity is whatever is making the wall hot.

Kind of a clumsy analogy, but the best I can do at this time.