I have read the paper with a lot of interest. I am not sure, though, that I understand the main
question posed in it: "is Zipf's law relevant to natural language", because
I don't understand what exactly "being relevant" means in this context.
Let me try to outline my own position on this issue.

There is a wide variety of opinions about power distribution laws,
ranging from "they certainly indicate complex-system behavior" to "they
have no meaningfulness at all".

I certainly disagree with both statements. Power rank distributions can
result from many different mechanisms, including the extremely simple
one, "random typing", which clearly defeats the idea that *every* system
exhibiting power-law distribution is complex. (This reminds me of
another grand claim: that every character sequence with long-range
correlations is "complex"). This
work confirms that random typing leads to (something like) power-law rank distribution.
Whether it is in quantitative agreement with distributions observed for
natural language (which it is shown here not to be) is immaterial for
this particular question.

On the other hand, I also disagree with the "Zipf nihilism" position
that claims that Zipf's law for language is simply not interesting just
because random typing models also exhibit Zipf-like rank distribution.
Whatever is the mechanism generating such distribution in language (in
my article cited here as ref [24], I argue that it may have to do with word semantics), it is
certainly *not* random typing, so random typing is simply irrelevant to
the question. Not being a proof though, this argument is a source of
doubt, because it demonstrates that simple causes *may* underlie power-
law rank distributions. And nothing would change if one demonstrated a
random-typing model producing exactly the same distribution as natural
language, because *the same distribution does not ensure the same
mechanims*!

The bottom line, to me, is this: the only was to make a claim that
Zipf's law for language is interesting, is to propose a specific
mechanism that generates power-law rank distribution in natural
language.

As for the differences between Zipf-like distributions resulting from
random typing vs. natural language, which are studied in this work, I
find them very interesting even outside of this debate. I would be
very much interested to see how the distributions change with the number
of words, what are the mechanisms producing large-scale deviations from
ideal power law, what determines the exponent, maybe what happens when
one progresses from Poisson processes to Markov chains, etc.