The headline makes it sound like the first modern era climate change extinction. The story is somewhat different. The Guardian headline would lead you to believe the the Puerto Rican coqui frog is extinct. Further reading shows that the frog (some varities?) is susceptible to the fungus Batrachochytrium dendrobatidis , which is causing population decline. Warmer temperatures aid the fungus spread and is making the males shorter, resulting in smaller higher pitched chirps which may not attract the females.
The chirps have been analyzed since 1986 and have been becoming higher. The concern is the females might not respond. Of course more study is needed.
As for extinction? It appears these frogs were introduced to Hawaii, where there are considered an invasive species. Perhaps we could return a few to Puerto Rico. The article seems to be a tad misleading. Just another climate skeer?