Thanks for asking this, it's super-important to understand it. If they're not infation-adjusted, then there's already been a (very slow) exponential reduction in the cost.
I think they are inflation-adjusted. Here's an inflation-adjusted source that explicitly lets you pick FY2021 dollars as the reference:
It puts the Saturn V at $5k USD/kg, the same as this article.
What's interesting is that it shows a general downward trend a little more clearly than this one does, but the Falcon 9 and Falcon Heavy are still very shocking outliers.
This seems to support it being adjusted not unadjusted. There is no unadjusted column and the Saturn V is listed as 5400 adjusted which lines up with the graph, if it were the unadjusted number it'd be ~7x off.
I think they are inflation-adjusted. Here's an inflation-adjusted source that explicitly lets you pick FY2021 dollars as the reference:
https://aerospace.csis.org/data/space-launch-to-low-earth-or...
It puts the Saturn V at $5k USD/kg, the same as this article.
What's interesting is that it shows a general downward trend a little more clearly than this one does, but the Falcon 9 and Falcon Heavy are still very shocking outliers.