Is it possible to make "finely ground corn flour"?
My answer here would be &quot;no&quot;. Even if it is not impossible, it is rather impractical to pursue this.
This may surprise some people, because as a home cook, it is pretty easy to take some grain and process it into small-sized particles. But what is difficult is to take some grain and process it into particles which are

very tiny
of consistent size
contain only the parts of the grain you want (typically the endosperm only, without the bran or the embryo)

Most instruments in our kitchens are not intended for grinding, and if you try them, the results are somewhat usable, but not especially good. To get really good quality fine flour, you need a precise mill and good sieves, plus the knowledge which sieve size to use at which step of the process.
In some applications, you could try just using the best grinding-like instrument you have lying around and see if you are happy with the result. This functions well if you want to do something like include unusual grain flours in a rustic bread. But this recipe (which looks amazing btw!) seems to be quite dependent on the proper flour texture and absorption ability. So I wouldn't bother trying it with the result of corn thrown willy-nilly into a food processor.