I don't understand US law nearly well enough, but aren't they essentially suing for future damages (e.g. something that hasn't happened yet)? How does this work as anything other than a PR stunt and a trophy-for-everyone move from a judge in Oregon?
Generally it's hard to pre-emptively sue to prevent the government killing you -- even though in the US the Constitution requires due process before a person can be deprived of "life, liberty, or property" -- because most ways the government has of killing you (guns, bombs, etc.) happen very quickly.
In this case the mechanism by which the government is alleged to be killing people is slow-acting enough that the people who claim they will be harmed have time to file a lawsuit.
Is it possible to sue and collect damages for exposure to carcinogens (eg. asbestos) before the cancer manifests? If so, there's a reasonable analogy to be made: once excess CO2 is in the atmosphere, solar radiation will inexorably cause harmful warming. The biggest difference is that carbon sequestration is somewhat imaginable, but still impractical (especially for non-government actors).
