I don't have real knowledge of gravity, but I can speculate a bit. First, I don't think the blackbox argument necessarily makes sense. If the black box contains a massive point particle, and this particle moves from the left side of the box to the right, then the gravitational properties certainly change. For example, if there is a particle on top of the box, it will initially be pulled to the left, and subsequently be pulled to the right.
Having said that, your intuition that photons should have gravitational influence makes sense, since according to special relativity, mass and energy are equivalent. Since total energy (mass + energy) is conserved, the gravitational influence of the photon should equal that of the electron-positron pair (assuming they are all located at the same position). I think the article is agreeing with this point of view.