Your math is right based on the summary but the article says:
"With a stable system and a turnover frequency of 360,000 moles of hydrogen per hour per mole of catalyst, the potential here is real."
Yes, but the specific numbers given would indicate 360,000 MOLECULES/hour, which makes it seem much more likely that the article itself misspoke by saying "moles" where it should have said "molecules"
Sanity check: 360,000 moles/hr per mole of catalyst = 100 moles/sec per mole of catalyst = 6x10^25 reactions/sec per molecule of catalyst.
You can't get a reaction time of 1/(6x10^25) sec = 1.7x10^-26 sec for chemical reactions in our current universe (maybe in a Big Bang)
1.7x10^-26 sec is FAR less time than it takes a photon to cross the width of a proton (and a proton happens to be an H+ ion)