What They Saw
They grew Azotobacter vinelandii DJ (an easy-to-transform strain) and knocked out hoxZ and hoxKG by transformation and screening for hydrogen production.
Comparing the hoxZ mutant to DJ (positive control) and the hoxKG mutant (negative control), they observed an intermediate rate of hydrogen oxidation, so there seemed to still be some activity. DJ consumed nearly all the hydrogen, and hoxKG consumed very little (the graph showed a decrease but it was apparently because gas leaked out of the vial, so it's a good thing they had good controls!).
Then they tried measuring short-term hydrogen oxidation with different electron acceptors: oxygen or methylene blue. DJ quickly oxidized all the hydrogen while reducing oxygen or methylene blue, as expected. Both mutants didn't show activity with either acceptor at first, despite the difference in the previous assay. But then they added sodium dithionite (a powerful reducer of oxygen) and more methylene blue, and the hoxZ mutant showed up to 80% of the activity of DJ. As far as I can tell, the hoxKG didn't show the same effect when they gave it the same treatment, but they don't say that explicitly. But it seems like the hydrogenase needs to be activated somehow, as by dithionite.
These results were confirmed by observing methylene blue color change too; DJ quickly started oxidizing hydrogen, but the hoxZ mutant did too after a longer lag period.
When they isolated membrane-bound hydrogenase from cells (still embedded in membranes), even DJ needed activation with dithionite. hoxKG mutants had no activity in any case, of course. But hoxZ mutant had more activity in the soluble supernatant portion than DJ did, at least when membranes were isolated aerobically; it seemed like lack of hoxZ led to more soluble enzyme. But it had low activity in general so this conclusion was uncertain. Though membrane-bound activity in general was higher when isolated anaerobically, and they didn't measure soluble activity in that case for some reason. So HoxZ may help stabilize hydrogenase in the presence of oxygen.
The increased presence of detached hydrogenase in the mutant was not confirmed by Western blot, so it seems like an artifact.
What This Means
HoxZ seems to have a role in shuttling electrons between hydrogenase and oxygen, though there may be other components involved in this path. It's possible that when HoxZ is missing, another acceptor can take the electrons, but isn't as good at it.
It also may be involved in activating the enzyme (which requires removing oxygen and providing reduction); somehow hydrogen is not enough for this. And it may help stabilize the hydrogenase to keep oxygen from inactivating it, maybe also using its role as electron transporter.