Could a gamma ray burst destroy life on Earth?

[Avalancheon]

Looking through the paper it is annoying that the authors don't explain that assumption, there are plenty of citations however so have you checked those?

Your maths is right but it is unclear from the paper if the authors were referring to total energy or the energy that reaches the ground (as most of the energy is absorbed by the atmosphere). The easiest thing to do to check is to just email the authors and ask for clarification on the assumption. It's quite common in academia to do this, so long as you are polite about it and do not take up too much of their time.

Sandburgs article stated that an energy level above 100 kilojoules per square meter would lead to an extinction level event. I think he got that impression from the Piran and Jimenez paper, which Brian Thomas cited. So in that regard, it seems like his study was a best case scenario for the Earth.

I'm also not sure whether or not the 100 kilojoule figure was the initial beam energy, or what reached the ground after atmospheric absorption. I'll send an email to the authors and ask them to clarify on this point, since its a key assumption.