The article makes it sound like the mystery of where the additional energy came from is the item of most significance, but we can probably safely assume that the "no free lunch" laws of thermodynamics still hold, and if we assume there's no new physics (I mean fundamental physics, not "Gee, we had no idea particles in microturbulent magnetic fields at high temperatures would behave this way") then the most interesting result is the ability to achieve temperatures of billions of degrees, because it's the inability to continuously maintain very high temperatures that has kept fusion from becoming a commercial possibility for power generation.
This is certainly the important point in all of this. And magnetohydrodynamics at these temperatures is the "new physics", not, as you point out, some new fundemental physics. I don't think we're tapping the vacuum energy yet
There is no point at all talking about these particular temperatures in relation to modifying decay rates on earth. If such temperatures could exist external of some extreme containment, there would be no earth to worry about!