This is a question about definitions. When two photons interact to create an electron/positron pair, does this process 'count' as annihilation of the photons? I've struggled to find a good definition of the term. Some places say that annihilation requires the end state to be electromagnetic radiation. But, on the other hand, I have found several text books which give annihilation processes ending in hadrons.
Annihilation is defined as the collision of a particle and its antiparticle resulting in the destruction of both. The conversion products do not have to be photons, but usually are because probability of products created is inversely related to mass, and photons are massless. In colliders like the LHC, this can be compensated for by smashing matter at higher and higher velocities in the hopes that matter-antimatter pairs coming out of the remnants have enough kinetic energy to then create particles more interesting than photons.
In two photon interactions, the photon coupling causes a fermion-anti fermion pair, such as electron-positron pairs as exploited in in Positron Emission Tomography(PET). The resulting annihilation is thus not a direct result of the photon coupling and is a distinct event.