In the good old times quantum computer used to be just a circuitry that processes qbits with gates that perform quantum operations (this is what can run Shor's

In the good old times quantum computer used to be just a circuitry that processes qbits with gates that perform quantum operations (this is what can run Shor's RSA breaking magic); D-Wave machines have nothing to do with this. As far as I understand the whole thing, they are just "solving" the minimization of some tunable potential function by just being pushed into such potential and allowed to relax to the lowest energy state -- it is like finding a lowest point of a hole by throwing a ball into it and looking where it stops (and being happy that it runs faster than a numeric code simulating the physics of such ball). The quantum part here is only the fact that quantum effects should help the search to escape local minima, but the speed-up mostly comes from the fact it is basically an analog device.