It's just slowly rotating billboards with cloud textures. Effective, but more of an animation illusion than anything approaching any type of cloud simulation.
Since this is a collection of 2D sprites in 3D space, we could call it "2.5D".
The rotation of the sprites really breaks the effect, though. Then again, having them still would probably be worse. What if the rotation for each sprite was random?
Works surprisingly well for the plain white cloud case, I guess that's the only one where additive blending works correctly. The other all have pretty glaring z-sorting issues. Still, impressive in plain CSS.
CSS 3D Clouds https://news.ycombinator.com/item?id=5193053 (February 9, 2013 — 294 points, 44 comments)
CSS 3D Clouds https://news.ycombinator.com/item?id=3744761 (March 23, 2012 — 17 points, 1 comments)