What animal could compete with us in any place on earth? What animal will adapt to a situation that we cannot? What habitat do we need to survive as a species (not 7 billion of us, but some number of us to survive as a species) that climate change can take away without scouring the entire earth?
This is where you're getting hung up.
We won't need an animal to outcompete us, when the ecological niches are all dying out and there's nothing left for us to eat, and we can't grow our own food because all the arable land is too hot to grow food, and all the regions where food could be grown aren't amenable to it due to not having hundreds of millions of years worth of plant growth living, dying, and decaying on them to create enough top soil to support life.
You've created a complete non sequitor that the ONLY WAY we can cease to exist is if we're OUT COMPETED by other species.
Species go extinct all the time without something else driving them to it.
And the habitat that can be taken away from us is the arable land, as I've already described, due to the lack of top soil and nutrients for intensive agriculture.
All you have to do, Cad, is look at North Africa and how hard it is to grow anything there, to understand what happens if the climate heats up 3-5 degrees over the next century.
We have enough technology to probably survive indefinitely on Mars if we could ship things there. We could ship dirt to northern areas for example, we could build huge greenhouses, etc. We aren't going to go extinct. Well, outside of nuclear war or a huge ass meteor strike.
Dude, the shipping dirt to northern regions to grow food thing is so crazy I can't even begin to fathom how you think that's possible. Top soil needs to be renewed on the regs. Right now we do that by dumping shitloads of artificial fertilizers on it.
This requires a complex technological human society to still exist in the first place. Also good luck shipping enough of it to cover enough of the ground to grow enough food to feed the people who are already starving due to the climate changing. Where will the energy come from to drive the transportation devices? More oil?
Sorry but this is silly season stuff here, Khalidbro.
Greenhouses will require sunlight and chemical fertilizers.
The scale we're talking about is science fiction levels. The whole of human society would be constructed solely around food production at this point.