According to their PR that I linked above (unfortunately, the badly translated version), the native wood is quite different from paper as speaker cone/dome materials. Here is a paraphrased summary:
(1) Wood has an ideal combination of high sound velocity ("fast" transients) and high intrinsic loss (low resonance) as a material for speaker diaphragm.
(2) Acoustic characteristics of wood are highly anisotropic (direction-dependent) due to the natural grains, which effectively prevents unwanted standing waves in the diaphragm.
Unfortunately, the maximum cone size they can manufacture is ~10cm (4") at this time. So, don't expect a beautiful 12" woofer just yet. Perhaps, a line-source array using a multitude of the 3" mid-woofers / 1" tweeters with a cabinet finished in matching birch wood veneers would look just awesome.