The units are weird, and the person writing the article seems to have conflated a few different quantities.
From the actual press release linked in the article:
Using our approach, power plants can generate five thousand kilograms of gold per year, per gigawatt of electricity generation (~2.5 GWth), without any compromise to fuel self-sufficiency or power output.
So unless I've also missed something, what they actually mean is 5 tons per year assuming a continuous power output of 2.5GW, which is roughly 22TWh of energy generation.
Or in slightly more approachable units, approximately 0.23g/MWh.