This doesn‘t make sense to me. Where is the “nonparametrical“ part?

He could just have the 2 variables transformed into ranks and used

the partial correlation procedure on the ranked variables. Whether it

is justified to treat a binary variable like an ordinal scale variable, I do

not know.

You wrote about categorical variables, did you mean dichotomous or

binary variables throughout?

With kind regards

Karabiner

By the way, the formulation of the result is annoying. “There was

no relationship“ is silly. Obviously, there was a relationship, the

coefficient is different from zero. It‘s just that it is not statistically

significant (which is not surprising given the low power of the

test , due to very small sample size).