Author here, thanks! I am not familiar with this website (science-news.co) so I cannot comment on the quality of the writing (or human origin). I agree with you that "prove" should be "predict" - they did not prove anything except that from a theory standpoint, this process can happen in quantum mechanics.

The sentence about lasers is also strange, I have no idea what is meant there. My only guess is that it might be trying to describe some laser experiment that uses lasers to "heat" a hohlraum to produce a field of photons. Then some other high energy photon beam is used to collide with the photons inside the hohlraum.

edit: Original article from DOE press release is here with a bit more info: https://www.bnl.gov/newsroom/news.php?a=119023