No need to put the term in quotes, the AdiZero jerseys are the authentics. I don't know how they stack up to the old Rebook ones since they're completely different designs but the point being is the AdiZero is the new authentic jersey.
The NHL shop has gradually degraded what they mean by authentic for about half a decade. It used to mean the exact same stuff that was on the ice.
I'm quite sure the AdiZeros in the team shop are not that even if they are pretty nice.