The simple approach in the article is no different if you imagine it as a negative binomial. The article does not assume any distribution, it's entirely nonparametric.
Non-parametric means more than just avoiding talk of distributions.
In my previous post I said "doesn't assume any distribution" I meant it doesn't depend on any particular distribution function.
But in the post above that I was sloppy and said "no assumptions about the distribution at all". Good catch.