Cardboard's ignition point is above 400C. Computer components don't do well running above 80C. Something would have to go horribly wrong for a computer to ignite cardboard. Cardboard just seems easy to ignite because it's commonly burned with a butane lighter that burns at over 400C as well.

I've got an i.MX6Q bare board running next to me. It's beefier than this book PC (quad A9s instead of one). It has no heatsink and gets only slightly warm to the touch after running it hard for a while.

If any excess heat is generated by this thing, that aluminum backplate can probably sink it.

As for UL certification, this thing is low-voltage DC only. The power brick should be certified but that's probably all that's needed. And FCC class-B like usual.

Case is "Recycled pressed cardboard with high-grade aluminum", so I'm guessing the paper is just on the outside of the real case.

Everyone who is moderately well read knows this is not a problem, see http://en.wikipedia.org/wiki/Autoignition_temperature