I have a decent amount of experience with flooring, as I've been working around it for the past few years. My impression is that this mop should not be used on hardwood, laminate, or cork. The fear is that it could cause your floor boards to swell from the added moisture and destroy the finish, or potentially warp the boards. I don't think any of the hardwood manufacturers would honor a warranty after this mop has been used on their products.
Maybe someone with more specific knowledge wants to chime in here and prove me wrong. I don't really know much about this specific product, but this issue has come up and my workplace's policy was to steer customers clear from steam mops for anything other than ceramics.