"Could you explain to me the "purely digital" nature of this process?"
You need a digital image file and a digital printer.to produce this dot pattern.
"Interference patterns aren't digital, are they?"
In this case they are. It seems to me you did not understand that paper. Interference as such is not digital, but in this case interference is applied digitally.
I've never heard structural color being described as "digital""
Structural colour is a rather new term. And I did not describe it as digital. But in this case structural colour is applied digitally.
"It certainly is an alternative process to produce colors
"
I did not question this.
I am busy with imaging systems and so far structural colour never got out of a tiny niche in photography. As attractive and simple it seems problems are envisible already. But Fischer with his couplers was as this stage too about 100 years ago, when he got stuck... And structural colour can yield amazing results.
In this very case the digital approach seems the promising way.