> Can you explain where Kuhn-Tucker enters the picture here?

If there are no constraints, then, sure, the Kuhn-Tucker conditions do not have a non-trivial role. In that case, commonly we would state up front that we were considering unconstrained optimization.

Sure, such a Lipschitz bound could give us some help on lower bounds on the objective function value but for those bounds we would need some constraints! Then at least in principle, we are back to the Kuhn-Tucker conditions again.

I suspect that the paper is (A) not about all of non-convex optimization but (B) about some of optimization, maybe some part of image recognition, where the objective functions are non-convex. So, we're talking a subtle language issue. Or the paper is about some parts of non-convex optimization!!!