If only it were humanity that was going extinct. I'd be happy to see 90% of mankind removed from the ecosystem to give it a chance of recovery. Sadly it will be a mass annihilation of every plant and creature by humans before we get to the point that the human population shrinks by any significant amount. We will be the last to go; driven no doubt to cannibalism to stay alive (Soylent Green anyone).
The planet will become one vast barren dust bowl, slowly burning away until it resembles Mars. Humanity will survive for a few decades after, using technology to live in hermetically sealed bio-domes. Maybe this is why Musk is making plans for Mars living. It is a practice run for staying alive on Earth until planet B can be found.
They say he is a smart fellow. Maybe he has worked out that climate destruction is inevitable and he is working on the technologies needed to leave the ruined uninhabitable earth behind and travel to the stars.