Any difference would be from the oil being more slippery, which would make it a percentage relationship. So if they had a 400HP V8 and got 8 more horsepower, that's 2%. On a 150 HP six would be 3 HP, which isn't significant in the real world. You can probably get that much or more by replacing a dirty air filter.
I'm always skeptical of that kind of test. Was the oil they took out fresh, with just a single dyno run on it? Did they use the same viscosity replacement oil? Did they correct both tests for temperature, barometric pressure and humidity? How many tests did they run back to back? Did they change the filter each time? Did they change anything else?
For the test to be valid they would have to change back to the original spec oil and test again. Then go back to the Royal Purple, then to the original, and so on for a dozen or so cycles, and at the end chart the results. If that protocol showed a consistent difference I'd believe it. A single test, especially from an unknown starting point, doesn't prove anything to me. And before I'd make a change on the basis of a power increase, I'd want to see the same experiment done running a hundred hours onto the oil, to see if the initial gains hold up.
All that said, for years tests have shown a slight power increase with synthetic oils, so I wouldn't call them charlatans, but I won't hang my hat on 2% until I see scientific test results. What you describe is an anecdote, nothing more.