From this, I would assume that any form of energy (not just rest-mass energy, but kinetic energy as well) would produce a gravitational force. Am I being too naive in my application of this equation, or is this a real thing?

I haven't made a formal study of General Relativity, but I do seem to recall from what I have learned about it that all forms of energy come in to the stress-energy tensor, which means that all forms of energy would also have an effect on the geometry of space, thus "energy would produce a gravitational force".