Never seen or ridden one, but chainless bikes have been around for over 100 years, and they have never gained a real foothold in the market. I don't see why this particular one would be any different. It doesn't appear to have improved in any meaningful way on the Columbia chainless bikes of the late 19 century.
The supposed benefits cited by the manufacturer sound somewhat ridiculous to me: you won't get grease all over yourself and won't lose a finger. Are they trying to say this is the perfect bicycle for someone who is prone to clumsiness?