What the question really amount to asking is, if (as LIGO said) the gravitational waves emitted from the black hole collision were emitted as 'pure energy' this surely means that they were emitted as photons. If this is the right interpretation does it therefore mean that when the waves interacted with the lasers at LIGO, were they self-interacting photons that were interacting with the lasers not 'ripples in spacetime'?
General relativity is a purely classical theory and it describes the emission of gravitational waves without involving gravitons, photons or indeed any other elementary particle. The energy in a gravitational wave is basically the self energy of the spacetime curvature. To use a rather crude analogy, you can imagine spacetime as an elastic material and the self energy is the energy required to bend it. A gravitational wave carries energy in an analogous way to a wave in an elastic material carries energy.
When you ask about what particles involved you are asking how we describe the gravitational wave, and the energy it carries, using quantum mechanics. Given that we have no theory of quantum gravity there isn't a firm answer to this. However if we attempt to use quantum field theory then we find gravitational waves are coherent states of gravitons just as light waves are coherent states of photons. Note that a gravitational wave isn't a hail of bullet like gravitons just as a light wave isn't a hail of bullet like photons. The relationship between the wave and particle is more subtle than that.
So there is no reason to invoke photons in considering interactions of gravitational waves. The interaction with the detectors at LIGO is essentially perfectly described using the purely classical approach of GR. If you wished to use a quantum description then you'd need to consider scattering of gravitons, though it's far from clear if this would be a useful approach.
This is flat-out incorrect:
the gravitational waves emitted from the black hole collision were emitted as 'pure energy' this surely means that they were emitted as photons.
Photons carry energy, yes, but that does not mean that all processes that carry energy do so through photons. In this specific case, the energy was emitted in the form of gravitational waves ("ripples in spacetime") which also carry energy, and which are entirely unrelated to photons.
To be clear, interpretations of the detection in terms of "self-interacting photons that were interacting with the lasers" are very much in direct contradiction with known physics.
As the comments and the two answers so far have mentioned, photons are the carriers of Electromagnetic Waves and Gravitons (supposedly) are the carriers of Gravitational Waves — please see this link for the carrier particles for each of the fundamental forces. This answer would, however, attempt to address how the "interference pattern" generated at LIGO could only be caused by the gravitational waves passing through it.
LIGO is engineered to be "blind" to EM and sound waves. See source.
All of LIGO's optical components reside in an ultra high vacuum chamber. A laser beam is first passed through a beam splitter, such that it splits the laser into two and sends each beam down along the two precisely identical L-shaped tubes. These laser beams are then incident upon the mirrors, from where they're reflected back to be detected by the detector at the base. This arrangement itself ensures that there will be no interference pattern where the laser beams recombine.
However, when the interference pattern is still detected, it means that there was the displacement of mirrors used in the setup, and not by the interference of any other light with the laser.
This displacement can arguably be caused by seismic activities too, but then it won't necessarily be detected at the other LIGO site, at least not with the same frequency and the exact time difference that it would take for a signal commuting at the speed of light (speed of gravitational waves) between the two sites.
In other words, it was the "spacetime" between the mirrors itself that experienced the distortion (because of shrinking and expansion of the distance between the mirrors and the detector as the gravitational waves passed through) and thereby generated the interference pattern thus observed.
The intensity of the recombined laser at the detector gives us the frequency of the gravitational waves and this was found to be exactly the same at both the LIGO sites in all the three events detected so far.