It used to be accepted that extinction of a species occurred with the death of the last member of that spices that represented a chance of reproduction in the wild. That being said, definitions of words change over time, same as trends and social norms. Things just change. And we eventually rewrite the definitions to accommodate that.

I don't think that it is particularly wrong to say an animal can be extinct in one region, while existing in another, but it it most definitly confusing to somebody who uses the traditionally accepted definition of extinct. It's much more concise to say that cheetahs disappeared entirely from the region, and only approximately 100 of their particular subspecies exist in the wild somewhere else. In fact, I would say that using the word 'extinct' in the way it is used in this post is most likely intentionally missleading- tho I appreciate that it is probably being done so to bring attention to an issue that I also believe needs to be taken more seriously be humanity on the whole.