As someone with a Ph.D. in physics, I found the whole article wrongheaded and partly wrong. Sure, Einstein's original paper (I did read it in its original German) did not have E=mc^2 in the short form, but don't worry, since it is still true. If you compress a spring, it weighs more. If you add a photon to a box, it weighs more. The net momentum of both does not matter here.