I think the strength/weight (specific strength) claims are questionable. They may be comparing it to a soft steel.
https://en.wikipedia.org/wiki/Specific_strength
To convert wood to Superwood, they REMOVE softer and hollow components, and compress the remainder. In the simplest model, the actual material does not become stronger, you just have more of it in a particular volume.
Cardboard is the reverse of Superwood. They take two pieces of paper, ADD space in the middle, which reduces the mass/volume, and makes it stiffer. But cardboard's specific strength remains the same as paper.
Compare it with piano wire (400) or carbon fiber (4000). To be ten times stronger than piano wire, Superwood would need to be 4000, or about the same as carbon fiber. I don't see Superwood claiming it's the same as carbon fiber.
However, the compression probably adds other effects that strengthen the material. It may line up the fibers so they don't buckle as easily. Removing soft material would allow adjacent fibers to buttress each other. It's possible that fibers bond in a new way. They may introduce 'alloying' materials.
Steels are very sensitive to micro structure, grain alignment, and alloying elements. Superwood is probably the same.