The innate, instinctual drive to maintain life is clearly a mindset, but it is more instinct. Their play, their interactions with each other, their self-cleaning behaviors, their use of dirt/litter to cover excreted waste, are understandably rooted in a desire to maintain life. That's all they do. They don't have jobs or sports teams. They just live.
An essential element of human thought is a sense of our mortality
No matter what we are doing or thinking, a comprehension (or perhaps it's often more of a confusion) of our human mindset is the mortality we recognize in our existence. From an early age, we go through life cognizant that it will end. Our actions and endeavors and interactions are predicated on the notion that our life, our physical being and more importantly our cognizance, will terminate. We work and love and write with the constant awareness that whatever we experience now will be a short experience. What we write will remain after we are gone, but will we have awareness of how that writing is received after we are gone? Does Mozart now appreciate how concert halls are filled with individuals playing and hearing his music? Does Shakespeare now take comfort in knowing his written works are some of the most treasured in human existence?
Our religious and spiritual formulations, which are distinctly human as far as we know, are rooted in a sense of our mortality. Mankind has from its earliest ages of cognizance created a mindset in reaction to our sense of our mortality. Our most distant ancestors watched each other die and be killed and were no doubt aware that their own lives would end. Their own thoughts would end. And in reaction to the accompanying fear, they developed theories of what happened to our minds after our physical bodies die and decay (the mind which is the root of our "souls," as the spiritual among us have created). That religious fervor is so omnipresent throughout human history exactly because of that sense of mortality.
And for those of us who believe in no higher being or soul that persists after death, the concept of that mortality is even more frightening. The more we realize that human existence is merely that, human, not divine, the more we learn of the vast unknowable depths of our cosmos, both in space and time, and how we and our planet and galaxy are such insignificant, almost infinitesimally small components of that cosmos, the more fearful are our notions of our mortality.
Once we die, our thoughts, our memories, all we have read and know about our history, all we have appreciated of music and art and science and literature, all we have seen of the wonders of our planet in the sky, the land, the sea, all of that thought, all the memories of our loved ones, all the pride in our accomplishments, all awareness of others' appreciation of those accomplishments .... just ends. Stops. Disappears entirely. The same sensation we had before we were conceived and born. We return to nothing.
This fearful notion of finality is what I'm not sure the cats are burdened with. They seem to live for the sake of living. But do they appreciate their mortality and does it frighten them too? They know that a coyote is to be avoided and no doubt realize in their instinctive way that the coyote will hurt and kill them. But is that animal awareness directed at prolonging life or is it truly an awareness of mortality? They know they must eat to live. But do they know what it means to die? Do they every day in the back of their minds have that notion of their finite time of existence? Or do they live without a pervading notion of death?