It is recursive descent. Scala's parser combinator library is beautiful, and has been, hour-for-hour, the most useful tool I have learned as a programmer. Parsing problems became so common once I understood how to parse things.

I'm writing my first compiled DSL right now, inspired by the sense that parser combinators gave me: "maybe you don't have to be a genius to write a compiler."

In addition to parser combinators, another great functional tool for dealing with recursive structures (e.g. abstract syntax trees) is recursion schemes. I've been banging my head against them this week, and I finally made some headway. They are useful for the nanopass technique referenced in the article.