Yes, it means that, metaphorically speaking --- "God" being a synonym for "nature."
To understand "natural rights" you first have to understand what is a "right." In the liberal and common law tradition, it denotes a certain relationship between a person and some thing (a property right) or a freedom to act in a certain way (a liberty right). For a property right, the relationship is that the person acquired the thing to which he claims a right "righteously," i.e., without inflicting harm or loss on any other person. For a liberty right, the act is "righteous" if it does not inflict harm or loss on any other person. A "natural" --- "God-given" --- property right is a right to things you acquired naturally, things you brought with you into the world, such as your life, body, various abilities, capacities, talents. A natural liberty right is the right to act in any way within your natural powers, provided you inflict no loss or injury on anyone else.
Well, moral agency has nothing to do with divinity or "God's image." The term just denotes creatures capable of formulating and understanding moral rules, and of recognizing other qualifying creatures as likewise so capable.Eusocial insects aside, I think the divinity of man, created in God's image, persists in an atheistic age. For you, it is called "moral agency". If we stop differentiating between humans and other animals, perhaps we can see that any natural rights that exist for humans may also exist for other animals. Many animals are clearly "moral agents" (although on a different level from humans).
https://en.wikipedia.org/wiki/Moral_agency
That's all true, but what sort of environments eusocial creatures seek out and how they respond to environmental variables is itself determined by their DNA. Eusocial insects do not have "free will."I'm not sure DNA "forces" anything. All behaviors result from a combination of nature and nurture; from genetic and environmental influences. This is true for humans and for other animals. If we step on an ant, its DNA won't force it to do anything but die.