Given that military training areas are de facto wild life sanctuaries I think that sonic booms have no lasting effect on wildlife.

You will still have termination shocks. In order to avoid a shock off the top of the top wing or the bottom of the bottom wing, the wings will have to tilt inwards so there is expanding flow around the outside (avoiding the shock). However the consequence of that design is that you will have 2 trailing shocks off the back of the vehicle as the flow re-compresses. If the plates are perfectly flat with respect to the flow streamlines, you will still have a shock as the boundary layer on the wing will trip the flow.
Also as shown in the flow configuration it has zero lift: the interior gemetry is identical top and bottom so the integration of pressures over both surfaces has a net of zero. There needs to be different shock angles to generate positive pressure.
Also neglects shock impingement aeroheating.

Forget about SSTs already. Boeing tried to interest the airlines in a faster (though not supersonic) airplane, the Sonic Cruiser. The airlines instead wanted to save on fuel costs and we got the 787 instead. I don't blame them. Until you can combine SST speed with subsonic fuel consumption... nothing will ever get built.

I know what supersonic is, and what subsonic is, but what is sub-supersonic? Is that the same as super-subsonic?

I don't believe that design will do MACH 1.

It should be clear to most that the diagram is only to explain the concept. The angles are clearly exaggerated and no representation of the final product.. I completely disagree with B@Man, this shape could easily get to mach speeds in thinner air. It can get to thinner air because of the increased lift of an all wing design and the extra wing..

When the article says that they can create lift with the Busemann wing, they mean 'some' lift. Not nearly enough to support an airliner in flight.
Adding any kind of structure to the Busemann wing will also create a shockwave and hence a boom. This includes engine pods, passenger compartments and control surfaces.
You could run a fleet of SSTs that were restricted to flying over water, and also in arctic airpaces in sparsely-inhabited Siberia and Canada. All this research is in a desperate attempt to speed travel across the USA, which is currently the biggest market. In 30 years (the earliest an airliner like this could fly) the market will have moved East where Supersonic travel can take place over water.

The claims made about wildlife are unproven and speculative.
A supersonic aircraft could be flown to an airfield away from heavily populated areas and then passengers could be transported by high-speed rail to the major cities and towns.
It would be nice if they end up building a unmanned demonstrator.

Clearly the ugliest aircraft concept in the last years. I would ran away if I see this!
How will it start or land? How will passengers enter the fuse?
The high complexity is a clear showstopper.
It's such a nonsense. It is heavy as hell, it has a drag as hell, it is inagile as hell, it is ridiculous!
There is a reason why we don't see biplanes or should i say "boxwings" in the air. Too complex, too heavy, too ... useless!

looks less like an airplane and more like a Romulan Warbird to me.