The actual paper is about realization of an algorithmically-designed optical device rather than optical switching. The device is "just" a computer-designed multiplexer.
With such a device an actual switch becomes easy: Make the device change the two inputs to be antiphase and combine them. If one of them is missing, the other passes through unphased (pun intended), but if both are present they cancel each other out; aka you have an xor switch!
Second, XOR is not a universal gate (even when combined with NOT). XOR can only sum things together (mod 2). For universal computation you need to be able to multiply (e.g. with an AND gate or a Toffoli gate).
There are limitations on how good the extinction (cancellation) can be based on how well the losses are matched in the respective waveguides.
In this case of this paper, I imagine that the phase relationship will be much more complex and it will highly wavelength dependent.