It is enclosed. They show a picture later and there's a green safety window to view the work piece in the machine, that material will be designed to block whatever wavelength of light the laser is using (most likely IR, and what do you know safety glasses for the IR bands are mostly green).
No. Such materials are designed to let through all but the narrow wavelengths expected of the laser. And some IR "shields" actually reflect IR light rather than absorb it. A proper laser shield should not be engineered to do the minimum necessary. Metal works. Wood works. Even blackout curtains bought at walmart can work.