The intuition behind the test is that if non-linear combinations of the explanatory variables have any power in explaining the response variable, the model is misspecified in the sense that the data generating process might be better approximated by a polynomial or another non-linear functional form.
The essence of this test lies in its ability to detect whether non-linear combinations of the explanatory variables have any predictive value in explaining the response variable. If they do, it suggests that the current model specification may not fully capture the underlying relationship, implying that a more flexible functional form, such as a polynomial or other non-linear relationship, might be needed.