“toughest challenges, such as world hunger or the dangerous effects of climate change” How does quantum computing address world hunger or climate change? Convincing humans to not use fossil fuels or to eat less beef doesn’t need Shor’s algorithm.
Regarding the world hunger and climate change claim. I think they are referring to the fact that quantum computers can simulate quantum chemistry more efficiently compared to classical computers. This article [0] talks about how quantum computers will be used for quantum chemistry; specifically nitrogen fixation.
[0]: https://cen.acs.org/articles/95/i43/Chemistry-quantum-comput...