@Destroy All Managers
I'm not sure I understand that much of it either. But they only seem to have written down an obvious Lagrangian for one possible particle ("We consider a massive spin-1 Abelian gauge boson X that couples nonchirally to standard model (SM) fermions...") and then fitted it using an effective theory. And, as they admit themselves (in the 3rd sentence you quote), that was the easy bit.
It's good that somebody's done the work. It's interesting to know this fits the data. It's an interesting direction. But it's not as ground breaking as the headline claims.
Biting the hand that feeds IT
