The standard model of particle physics has a quantum mechanical Lagrangian where the elementary particles of the table enter as point "particles" with the mass and the quantum numbers in the table. This is a very successful physics model fitting an enormous amount of data from resonances organized in the eightfold way , to LEP data with the culmination of the Higgs discovery at LHC .
"Particles" with quotation marks because they are not classical billiard balls, they are quantum mechanical entities manifested in experiments microscopically with probability distributions.
The reason one calls photons and gluons and gravitons and Z and W particles is because of the validation of the standard model.
The above is the current state of particle physics, experiment and the theory that describes them and can predict new behaviors.
The photon emerged as a particle, at the time not separated from a classical particle because of the photoelectric effect. It was a proof that light was composed by quanta and these were named photons, to finally be called quantum mechanical entities, "particles". With quantum field theory the emergence of the classical electromagnetic radiation from the photon field is shown in this blog post of @Motl.