Of course it is quantum. The whole universe, including the reactions in the D-Wave are based on the laws of quantum mechanics. Regular computer chips have to take quantum effects into account too, although they try to defeat quantum effects rather than utilize them. Nevertheless, at a basic level the transistors work because of the laws of quantum mechanics.
So how do you want to describe the D-Wave? Do you want to describe it using the laws of Quantum Mechanics? Or do you want to approximate it using a classical model that is carefully chosen to not get the quantum effects wrong?
In either case, as the article says, it's still fast.