Nelder-Mead in effect does a gradient descent. By evaluating the function at the vertices of the simplex, it figures out approximately the direction of the gradient and uses that to determine the next evaluation. So it is quite similar to steepest descent.

Hooke-Jeaves also is similar to gradient descent because it evaluates points near the best current estimate of the minimum.

So despite the fact that they are derivative free, it seems to me that they behave similarly to gradient descent.