Photons may not interact with themselves much, but they interact with other materials in significant and useful ways, and there are plenty of materials that change their optical properties in response to an electric field (which can be either electronic or optical in origin, given that light, particularly coherent light can have fairly strong electric fields).
There are millions of things that an electronic digital computer can do that are unlikely to be replaced by photonics, but a hybrid approach may offer advantages in computing specific things. As we have slowed down getting perf/watt advantages from shrinking processes, more and more specialized hardware has been used for performing calculations. It's not that far-fetched to think that photonics might have a niche where it has performance advantages.
You're right that photons interact with many materials. However, few exhibit semiconducting properties that's useful for building logic gates.
Silicon has a kind of perfect energy band gap for its valence band electrons jumping to conducting band free elections to allow electricity flow. The gap is not too small to introduce ambiguity or too big to require too much energy to move from non-conductive to conductive state. Photonics needs to find a semiconducting material/alloy that beats silicon to be a viable option.
Most research in building logic gate with light is a combination of light and electricity. The most promising recently is using Josephson junction in a superconducting electric current loop. A photon hitting the loop adds energy to the superconducting current. With enough energy the current becomes critical current, which moves the Josephson junction from 0 voltage to a voltage. The raised voltage gives off the energy and the current falls back to non-critical. Continuous photons hitting the loop causes the Josephson junction to have an extremely high frequency AC voltage. That's a photon controlled gate.
But the research is still really early and it requires low temperature superconductivity. It's still a long way to be competitive in reality.
I think we are both in agreement that photonics will not replace silicon for logic gates (at least with current technology). However both what I was talking and in the specific example from TFA photonics are being used for analogue computing which does not necessarily require logic gates.
The simplest example would be AM modulating a laser with a signal and passing the result through a prism. This calculates a Fourier transform on the signal. This is not a great example because, for most domains, the output is too noisy to be of great use and ADCs/DSPs can do this fairly efficiently already. I believe the computer mentioned in TFA involves matrix projections.
There are millions of things that an electronic digital computer can do that are unlikely to be replaced by photonics, but a hybrid approach may offer advantages in computing specific things. As we have slowed down getting perf/watt advantages from shrinking processes, more and more specialized hardware has been used for performing calculations. It's not that far-fetched to think that photonics might have a niche where it has performance advantages.