How to get the loadings (COEFF) as in linear PCA?
How to know the variables of highest impact on a component?
NLPCA cannot give you a single loading or COEFF vector, instead to each point on the curve the contribution is different according to the direction of the curve. For example, if your curve represent a time series, you can have some features having an impact at early times and other features having high contribution at later times: this means at any point on the curve you get a different COEFF vector.
Fig 2.11 in http://pca.narod.ru/2MainGorbanKeglWunschZin.pdf shows a possible discussion about the impact of features (metabolites) along a curved nonlinear component.
A time-point dependent loading vector can be calculated by a gradient/tangent on the curved nonlinear component, in case of a single k=1 time related component.