Also, that looks like a structural nightmare to build, and the weight on the tires will require special tires, at best...
It's just a quad tandem. They're pretty uncommon so they tend to be built-to-order (and very expensive), but they're common enough that they're not "experimental" or anything and there are companies that specialize in them (e.g. Santana, Co-motion).
Also, as far as the frame being a "structural nightmare" goes, look at it again: it's basically just almost a normal diamond-frame (except with single tubes instead of split seatstays and chainstays) repeated several times. It's not complicated, just big.
Although they use higher-spoke-count wheels, I would expect most tires to survive perfectly fine: you'd just inflate them to the top end of the PSI range, but the contact patch would more resemble the bottom of the PSI range ( contact patch size per tire = gross vehicle weight / (2 * tire pressure) ). Remember, lots of wheels are built to take the abuse of things like mountain-biking and cyclocross; I doubt that a large tandem stresses them any more than that kind of thing. Super-thin lightweight racing tires might not be a great idea, of course.
Here's what
Santana has to say about tires and wheels on their quad/quint/hex tandems:
Wheels: Hadley/Velocity Dyad 48 spoke
Tires: Continental Gatorskin 700x32mm or Travel Contact 26x1.75" steel bead
Choice of 700c wheels limited to 650 lbs combined rider weight or 26" wheels allowing up to 1050 lbs CRW.
By the way, Sheldon Brown has a good article about
DIY tandems, although his technique of grafting two normal bicycles together might not be good enough to scale to a quad (because you might want to build the frame out of larger-diameter tubing, etc.).