Can you imagine being that last human? Chances are they'd not realize the importance of that breath. Chances are no other species or thing would either. In the grand scheme of things it would just be another moment. We put such an inflated amount of importance on ourselves.
Of course, that wouldn't be the end of the human race really. The effects we have on the world, from our buildings to climate change, would last on for much, much longer. We've changed the course of rivers, built asphalt seas miles upon miles wide, touched the sky with our buildings, altered the DNA of other living creatures, and possibly created both the largest desert and the largest rainforest on Earth. Climate change has reached the point that some scientists believe is irreversible. On an individual level, sure, we have an inflated importance, but our effects on the Earth, and maybe someday, the Universe at large, will last until the end.