For the record white oak isn't one of the hardest woods as the ad states. It is, however, pretty dense. I would view a high level of hardness as a liability in a speaker cabinet. Very hard cabinets would simply tend to resonate more easily than less hard materials and resonance isn't something desirable in a speaker enclosure.
High density, however, is OK in a speaker enclosure and white oak should be fine, not because it is hard, but because it is dense. However, I can't see how it would be any better than a hardwood plywood or MDF, both of which are more uniform and predictable. Certainly the fact that whisky was aged in it would meaningless. The wood would be dried before use in manufacturing a speaker enclosure.
A California bicycle manufacturer released a bike frame made of bamboo late last year. Bamboo doesn't make a particularly good bike frame material but the marketing gimmicry was interesting and effective. I would put these speaker enclosures in the same gimmic-ridden category.