Has there ever been a period in Earth's history where CO2 concentration in the atmosphere changed this quickly without being accompanied by mass extinctions?
The Paleocene-Eocene thermal maximum is actually a great analogue for what we're currently experiencing. Huge increase in global temperature over a relatively short period of time, probably due to runaway methane release. It went back to normal within a few hundred thousand years because of increased planktonic CO2 sequestration in the expanded tropical zone.
I think the point isn't so much that Earth will heat up but that it will do so at a tremendous pace (in geological timescales). Nature can't adapt so quickly. Basically it will lead to a mass extinction simply because of how quickly it is happening. Nature takes a longer time to genetically adapt to a changing environment than humans have even existed. That's the problem.
Take the rate of change by time of that curve and plot it, you'll see a massive spike during today, And a line that bounces around zero for the rest of timeframe.