Generally speaking, with the way people use the term *nonparametric* to decribe a model, if you had more data points, there would be more parameters, generally without an upper limit. It doesn't mean "has no parameters" nor is it required to be infinite-parametric with a finite sample size.

To take a different example, consider say spline models. Even though with some given sample you could give a list of parameters and their estimates (that is, after all, how you calculate the smooth fit), it is still *nonparametric* in this sense of the word.

Similarly nonparametric distributional models for continuous data can be based on things like the ecdf itself or on a histogram or on a KDE. In particular note that with the KDE, even though for a given kernel family (say Gaussian), the kernel itself is "parametric" in the sense that it has a single parameter, the density estimate itself is not fixed-parametric. 

In each such case, the number of parameters is not fixed and will generally grow with sample size (not always linearly).