Cool video. That's an interesting demonstration of wave interaction. It's just a phased array with all the sources pointed inward at each other. You could do the same thing in air with an array of speakers. I can't imagine air would work to create the kinds of temperatures and pressures required to make diamonds, though.
There are engineering/physics software packages that can simulate wave interactions like this. Here are phased array examples using COMSOL, and MatLab. You might be able to approximate the behavior in a FEA or CFD tool, too. Setting up the model is not a trivial exercise, though.
Your idea of arranging energy sources in a sphere, focusing their energy inward toward the center, reminds me of implosion-type nuclear weapons. That's basically how they work.