Spearman correlation can indeed be used to compute the nonlinear correlation :
- between two variables
- if there is a strict total order for each one of these variables (otherwise it is impossible to determine the ranks).

Thus, in the most general case (i.e. if one of these two assumptions is violated), we cannot compute the Spearman correlation anymore.

Furthermore, even if the assumptions hold, if the relationship between the two variables is non-monotonic, using the Spearman correlation is possible but irrelevant : the Spearman correlation for the quadratic function I presented in the article would still be 0, for example.