You already know that this is a new, largely unsupported resolution to date so I won't repeat... My opinion is that it's really meant for people in offices who want to run several spreadsheets and other kinds of business/document pages side by side without having to go the multimonitor route. What happens if you set your desktop to 2560x1080 and then run the game...? You could try that --but still, I think you are going to have serious aspect ratio problems...as obviously the game (any game, really) is not done @ 21:9 resolution, but @ 16:9, or 16:10 (1920x1200 is my resolution for the game.) I think you are going to have to settle for an aspect-ratio *correct* 1920x1080 resolution, which will mean you'll have sizable black borders to either side of the game screen. But I don't think that can be helped.
Well, I do understand a lot of games don't support this, altough the engine support this, so it shouldn't be that big of a issue.
And as jawls said, it says it supports this resolution...
Sources:
http://pcgamingwiki.com/wiki/Pillars_of_Eternity
http://community.pcgamingwiki.com/page/blog/_/features/port-reports/pc-report-pillars-of-eternity-r180
(runs 2560x1600 so my resolution shouldn't be a problem, aspect ratio isn't the issue here as it crops the image, not scales it.).
http://steamcommunity.com/app/317120/discussions/0/35221584572096801/
(public beta got it to work in windowed mode).
So while you are correct in that a lot of games do not support ultra-widescreen - this game surely does, altough it seems to have some issues on linux. Please don't post stuff like that if you're not helping us out with suggestions.