The new chemical treatment essentially removes the lignin from wood. The precise nature of the process isn't mentioned in the paper, which suggested it might be nightmarishly complex or involve extremely toxic chemicals.

I'll go on a limb and assume that treatment of wood is some derivative of Kraft process (one for making paper pulp), likely using sodium hydroxide and sodium sulfite to chop the lignin to make it easier to remove. Boiling in hydrogen peroxide (with or without metal catalyst) further degenerates pre-shredded lignin via an analogue of Dakin reaction, which is also well understood – and is especially efficient against free-phenolic bits of lignin obtained in most variants of Kraft process.

What's left is likely susceptible to moisture, as the original publication makes it a point worth mentioning numerous times. You let that cellulose soak up too much water, and there goes your structural strength. They even had to treat it in fluorosilane to make it superhydrophobic when testing outdoors. In Arizona.

It's damn interesting, but I'm sceptical about it being viable outside of extremely arid places.

EDIT: Here's a great video explaining similar chemistry behind making transparent wood, which IMHO is a fascinating material: