Your doubts on the flowchart are well founded. It is no more than a bunch of boxes connected with arrows.
Put simply: nonparametric, semiparametric, and parametric tests represent a gradient of stronger assumptions and, consequently, stronger inference. They have more to do with the distributions of the data than with the way that the data are measured.
Indeed, a simple example of an efficient fully parametric test for nominal data is the simple Pearson Chi-square test of independence. We use a fully specified binomial likelihood for the response.
Ratio data provide the perfect rationale for a non-parametric test. For instance, the ratio of two normally distributed random variables is Cauchy distributed, and Cauchy random variables have nonfinite mean or variance*. In that case, the log-rank test is a highly powered test for differences in median which is a well defined measure of location for a Cauchy-location family of distributions.
*finite mean and variance are the most critical assumptions behind the T-test, a general test for mean differences which is commonly what is referred to as a parametric test, even though it makes no actual distributional assumptions. In either case, the normal probability model is wrong anyway.