I would have to presume that the adaptor replaces one or more of the (fairly generic) spacers/locking nuts on the axle assembly.
That's what I first thought, but it's designed to fit with the flanges outside the dropouts rather than inside, so no need to adjust the spacing. the only think I can think of is a bit of H&S safety margin kicking in – C&C hubs tend to have slightly longer axles; although there shouldn't be a problem with using a standard QR and axle on this: the difference between a steel and an aluminium dropout is easily as significant.
If so the piece on the RHS will do nothing to stop the hub moving under braking.
Well, no – it's a tug, for tensioning the chain and stopping it moving under pedalling load.
I'm struggling slightly with figuring out the adjuster on the brake plate, though…